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<div class="chlinktop"><span class="chlink1">Goto Chapter: </span><a href="chap0.html">Top</a>  <a href="chap1.html">1</a>  <a href="chap2.html">2</a>  <a href="chap3.html">3</a>  <a href="chap4.html">4</a>  <a href="chap5.html">5</a>  <a href="chap6.html">6</a>  <a href="chapInd.html">Ind</a>  </div>

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<div class="ChapSects"><a href="chap1.html#X808DC49C7ED99B52">1 <span class="Heading">Monoidal Categories</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X808DC49C7ED99B52">1.1 <span class="Heading">Monoidal Categories</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X84997A1E8188D6BE">1.1-1 TensorProductOnMorphisms</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X85008BF07C2C0386">1.1-2 TensorProductOnMorphismsWithGivenTensorProducts</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X84C2FAEA7B9678AA">1.1-3 AssociatorRightToLeft</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X85645C4D86060ED2">1.1-4 AssociatorRightToLeftWithGivenTensorProducts</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7C5A064C7E1995F1">1.1-5 AssociatorLeftToRight</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7C59D73F8389E389">1.1-6 AssociatorLeftToRightWithGivenTensorProducts</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7EBCAFDD81BDB655">1.1-7 LeftUnitor</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7ED284DF7BA21774">1.1-8 LeftUnitorWithGivenTensorProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X79A274078147A9F7">1.1-9 LeftUnitorInverse</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X849609447CAE996B">1.1-10 LeftUnitorInverseWithGivenTensorProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X82F758CB7A23468A">1.1-11 RightUnitor</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X84C8F97F7BF2282D">1.1-12 RightUnitorWithGivenTensorProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X82DC825480E87301">1.1-13 RightUnitorInverse</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X85A8A87C87B33008">1.1-14 RightUnitorInverseWithGivenTensorProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X797034F17AA47EE0">1.1-15 TensorProductOnObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7BF7FFDF8789474A">1.1-16 TensorUnit</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X7FB8551A815BEC53">1.2 <span class="Heading">Additive Monoidal Categories</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7ACF268E7D82B0C9">1.2-1 LeftDistributivityExpanding</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7CA18968862D2285">1.2-2 LeftDistributivityExpandingWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X780322FE7E5A626D">1.2-3 LeftDistributivityFactoring</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X784D8CD685F5F021">1.2-4 LeftDistributivityFactoringWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8409C74778A4313A">1.2-5 RightDistributivityExpanding</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7DBE629F811DEADC">1.2-6 RightDistributivityExpandingWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X86C5C33786C1DC28">1.2-7 RightDistributivityFactoring</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X795267217F7807CE">1.2-8 RightDistributivityFactoringWithGivenObjects</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X7D94AD967E6D60F1">1.3 <span class="Heading">Braided Monoidal Categories</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7C6ADBFE7A8DD1E3">1.3-1 Braiding</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7F4B09A87B2500C0">1.3-2 BraidingWithGivenTensorProducts</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8195EC5279D3E8D0">1.3-3 BraidingInverse</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X854AFBC67C836769">1.3-4 BraidingInverseWithGivenTensorProducts</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X85ED71067F7CEA82">1.4 <span class="Heading">Symmetric Monoidal Categories</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X85035E9683B050D0">1.5 <span class="Heading">Left Closed Monoidal Categories</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X87A4C0637EB8A18E">1.5-1 LeftInternalHomOnObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8439FF407D2C9C6E">1.5-2 LeftInternalHomOnMorphisms</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7861C2AD82F62C77">1.5-3 LeftInternalHomOnMorphismsWithGivenLeftInternalHoms</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X82C4FACF83C3611D">1.5-4 LeftClosedMonoidalEvaluationMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8575A3748713EACF">1.5-5 LeftClosedMonoidalEvaluationMorphismWithGivenSource</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7A526C59812F2A59">1.5-6 LeftClosedMonoidalCoevaluationMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7BC7F1497A00E87A">1.5-7 LeftClosedMonoidalCoevaluationMorphismWithGivenRange</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X83A5A47979C9B92D">1.5-8 TensorProductToLeftInternalHomAdjunctMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7BB734AA7F213B47">1.5-9 TensorProductToLeftInternalHomAdjunctMorphismWithGivenLeftInternalHom</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7C7D769879A7DA90">1.5-10 LeftInternalHomToTensorProductAdjunctMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X80431C73861AEC43">1.5-11 LeftInternalHomToTensorProductAdjunctMorphismWithGivenTensorProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X79AC308B847F5177">1.5-12 LeftClosedMonoidalPreComposeMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X78E3E67480AC81F4">1.5-13 LeftClosedMonoidalPreComposeMorphismWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7CFBE32D7F8F16CD">1.5-14 LeftClosedMonoidalPostComposeMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7D5E05257D908A56">1.5-15 LeftClosedMonoidalPostComposeMorphismWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X859959ED7F2CFDCC">1.5-16 LeftDualOnObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7B697FFC7B23A48B">1.5-17 LeftDualOnMorphisms</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8282E454874316D8">1.5-18 LeftDualOnMorphismsWithGivenLeftDuals</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7FF3227087ABDA8E">1.5-19 LeftClosedMonoidalEvaluationForLeftDual</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X86995E4D7A63E68F">1.5-20 LeftClosedMonoidalEvaluationForLeftDualWithGivenTensorProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X85D2B94A85E3DBD5">1.5-21 MorphismToLeftBidual</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X868774B68189D7E9">1.5-22 MorphismToLeftBidualWithGivenLeftBidual</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7939CEE8854017D2">1.5-23 TensorProductLeftInternalHomCompatibilityMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X798C160A84CA5623">1.5-24 TensorProductLeftInternalHomCompatibilityMorphismWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8635D47E7835C8AA">1.5-25 TensorProductLeftDualityCompatibilityMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8435799E83221130">1.5-26 TensorProductLeftDualityCompatibilityMorphismWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X80FE157E81B02827">1.5-27 MorphismFromTensorProductToLeftInternalHom</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X78FDDC2986E50825">1.5-28 MorphismFromTensorProductToLeftInternalHomWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7EA425DA848670D9">1.5-29 IsomorphismFromLeftDualObjectToLeftInternalHomIntoTensorUnit</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X781A2D417A8BC8DF">1.5-30 IsomorphismFromLeftInternalHomIntoTensorUnitToLeftDualObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X82D9D78C7A8DA61A">1.5-31 UniversalPropertyOfLeftDual</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7C7A252A78484873">1.5-32 LeftClosedMonoidalLambdaIntroduction</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X83B3A8FA8363F620">1.5-33 LeftClosedMonoidalLambdaElimination</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7ECAB43778388C41">1.5-34 IsomorphismFromObjectToLeftInternalHom</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X874D7D8E81A6AFF1">1.5-35 IsomorphismFromObjectToLeftInternalHomWithGivenLeftInternalHom</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7908CF267DDAA38C">1.5-36 IsomorphismFromLeftInternalHomToObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7B2F235C8444803C">1.5-37 IsomorphismFromLeftInternalHomToObjectWithGivenLeftInternalHom</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X7BC682067A30E580">1.6 <span class="Heading">Closed Monoidal Categories</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X78AA83E77B380D68">1.6-1 InternalHomOnObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7C0191A483A72F98">1.6-2 InternalHomOnMorphisms</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X861226B47B5CB713">1.6-3 InternalHomOnMorphismsWithGivenInternalHoms</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X844F05DF7DE23F99">1.6-4 ClosedMonoidalRightEvaluationMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X83E6461280B0EB0C">1.6-5 ClosedMonoidalRightEvaluationMorphismWithGivenSource</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7A745E5A836B5E91">1.6-6 ClosedMonoidalRightCoevaluationMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X868AD1A278EBAB03">1.6-7 ClosedMonoidalRightCoevaluationMorphismWithGivenRange</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7BA9C4A184346304">1.6-8 TensorProductToInternalHomRightAdjunctMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8218B01287CD44E5">1.6-9 TensorProductToInternalHomRightAdjunctMorphismWithGivenInternalHom</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X78A16762823E5F1C">1.6-10 TensorProductToInternalHomRightAdjunctionIsomorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X81D37FA282FC8F11">1.6-11 TensorProductToInternalHomRightAdjunctionIsomorphismWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8271B2767A2DFE76">1.6-12 InternalHomToTensorProductRightAdjunctMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7ACBB0CE7FA4C781">1.6-13 InternalHomToTensorProductRightAdjunctMorphismWithGivenTensorProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X79EEE4757C27C26E">1.6-14 InternalHomToTensorProductRightAdjunctionIsomorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7B4CD74A7CE51263">1.6-15 InternalHomToTensorProductRightAdjunctionIsomorphismWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X80B3C53A854B515B">1.6-16 ClosedMonoidalLeftEvaluationMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X84E1E136819BDA89">1.6-17 ClosedMonoidalLeftEvaluationMorphismWithGivenSource</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7E35DEB787A71A1F">1.6-18 ClosedMonoidalLeftCoevaluationMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8196CE5D7C88D83C">1.6-19 ClosedMonoidalLeftCoevaluationMorphismWithGivenRange</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X80A58B1F80A186BD">1.6-20 TensorProductToInternalHomLeftAdjunctMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7CCE373482D60A57">1.6-21 TensorProductToInternalHomLeftAdjunctMorphismWithGivenInternalHom</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X793BAA50819573E4">1.6-22 TensorProductToInternalHomLeftAdjunctionIsomorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X791276987824CDF8">1.6-23 TensorProductToInternalHomLeftAdjunctionIsomorphismWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X85F426677EB81BCF">1.6-24 InternalHomToTensorProductLeftAdjunctMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X859B738881052D1C">1.6-25 InternalHomToTensorProductLeftAdjunctMorphismWithGivenTensorProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X86AD79F17F8CEE96">1.6-26 InternalHomToTensorProductLeftAdjunctionIsomorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7D707B26863D508A">1.6-27 InternalHomToTensorProductLeftAdjunctionIsomorphismWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X86E4E97C82BFB45C">1.6-28 MonoidalPreComposeMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7FE4A52284060F20">1.6-29 MonoidalPreComposeMorphismWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X79F4FCE781385829">1.6-30 MonoidalPostComposeMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7E6933B8816EE4E3">1.6-31 MonoidalPostComposeMorphismWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X80FFC71D7E57DD53">1.6-32 DualOnObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X815C0BC47D000819">1.6-33 DualOnMorphisms</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7DCC0F468386AA46">1.6-34 DualOnMorphismsWithGivenDuals</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X86D42C7587F03A68">1.6-35 EvaluationForDual</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7B588B1B8472834E">1.6-36 EvaluationForDualWithGivenTensorProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7F68B55781C1DFB1">1.6-37 MorphismToBidual</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X79260E5680F1E741">1.6-38 MorphismToBidualWithGivenBidual</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X80CDA0CB821E08EE">1.6-39 TensorProductInternalHomCompatibilityMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7B0194A07AB73486">1.6-40 TensorProductInternalHomCompatibilityMorphismWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7D173DB08132E40A">1.6-41 TensorProductDualityCompatibilityMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X794ED97782B8DF76">1.6-42 TensorProductDualityCompatibilityMorphismWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8439BFF57BFE390F">1.6-43 MorphismFromTensorProductToInternalHom</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8473D28B7F3A5E20">1.6-44 MorphismFromTensorProductToInternalHomWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8430726C82D6CFF7">1.6-45 IsomorphismFromDualObjectToInternalHomIntoTensorUnit</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7A015736812A97C6">1.6-46 IsomorphismFromInternalHomIntoTensorUnitToDualObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7AF8F68887146C20">1.6-47 UniversalPropertyOfDual</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X80F3F2287B9E55E3">1.6-48 LambdaIntroduction</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X79EC44077F661E80">1.6-49 LambdaElimination</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8726BA888787D53D">1.6-50 IsomorphismFromObjectToInternalHom</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X87F91EF37C76A7F7">1.6-51 IsomorphismFromObjectToInternalHomWithGivenInternalHom</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X831CF4E1824FA178">1.6-52 IsomorphismFromInternalHomToObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7988DC7C79BED3B2">1.6-53 IsomorphismFromInternalHomToObjectWithGivenInternalHom</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X86546D277A535EB1">1.7 <span class="Heading">Left Coclosed Monoidal Categories</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7CE5D10B7F10E9CC">1.7-1 LeftInternalCoHomOnObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X853213767BB48099">1.7-2 LeftInternalCoHomOnMorphisms</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7F302E3880752A2F">1.7-3 LeftInternalCoHomOnMorphismsWithGivenLeftInternalCoHoms</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X819A762D83B1C294">1.7-4 LeftCoclosedMonoidalEvaluationMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7E5607B1789E00B7">1.7-5 LeftCoclosedMonoidalEvaluationMorphismWithGivenRange</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X81A249CE84828A9D">1.7-6 LeftCoclosedMonoidalCoevaluationMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7D1018A284F21140">1.7-7 LeftCoclosedMonoidalCoevaluationMorphismWithGivenSource</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X851216B2807B3900">1.7-8 TensorProductToLeftInternalCoHomAdjunctMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X87BFA0FA7AFF2868">1.7-9 TensorProductToLeftInternalCoHomAdjunctMorphismWithGivenLeftInternalCoHom</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7DDDACD58454C3A4">1.7-10 LeftInternalCoHomToTensorProductAdjunctMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X821AC96981CA794C">1.7-11 LeftInternalCoHomToTensorProductAdjunctMorphismWithGivenTensorProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8416357982DCBEE4">1.7-12 LeftCoclosedMonoidalPreCoComposeMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7EECDE4583E14A59">1.7-13 LeftCoclosedMonoidalPreCoComposeMorphismWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X80A270E982F5BC2D">1.7-14 LeftCoclosedMonoidalPostCoComposeMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X867C6F087D72AB3F">1.7-15 LeftCoclosedMonoidalPostCoComposeMorphismWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X85A63AA57F0678EE">1.7-16 LeftCoDualOnObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7949DE307D2D5083">1.7-17 LeftCoDualOnMorphisms</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X84C835CB7E708596">1.7-18 LeftCoDualOnMorphismsWithGivenLeftCoDuals</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7A20AC6A837F79BA">1.7-19 LeftCoclosedMonoidalEvaluationForLeftCoDual</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X87B15AC678955783">1.7-20 LeftCoclosedMonoidalEvaluationForLeftCoDualWithGivenTensorProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7F67676A85A47BDB">1.7-21 MorphismFromLeftCoBidual</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7AF5F77180E09AAE">1.7-22 MorphismFromLeftCoBidualWithGivenLeftCoBidual</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X84331A1B7F62782F">1.7-23 LeftInternalCoHomTensorProductCompatibilityMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X808BEB0879D58CAF">1.7-24 LeftInternalCoHomTensorProductCompatibilityMorphismWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7B4A66A8803C99BA">1.7-25 LeftCoDualityTensorProductCompatibilityMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X86E72092788A8F2D">1.7-26 LeftCoDualityTensorProductCompatibilityMorphismWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7A5FDE4B83C5F328">1.7-27 MorphismFromLeftInternalCoHomToTensorProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7BD2A33F84A2FBAB">1.7-28 MorphismFromLeftInternalCoHomToTensorProductWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7CC10C9E7EA7EED4">1.7-29 IsomorphismFromLeftCoDualObjectToLeftInternalCoHomFromTensorUnit</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X87F96B047F320A17">1.7-30 IsomorphismFromLeftInternalCoHomFromTensorUnitToLeftCoDualObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7A0DE1667FF28457">1.7-31 UniversalPropertyOfLeftCoDual</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X85960F7479FFA8DA">1.7-32 LeftCoclosedMonoidalLambdaIntroduction</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8721DDEC7DF9D89D">1.7-33 LeftCoclosedMonoidalLambdaElimination</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X853342457CC3B489">1.7-34 IsomorphismFromObjectToLeftInternalCoHom</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X82709BED807CB6FC">1.7-35 IsomorphismFromObjectToLeftInternalCoHomWithGivenLeftInternalCoHom</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X806C843B82108148">1.7-36 IsomorphismFromLeftInternalCoHomToObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8370164B7EAF833D">1.7-37 IsomorphismFromLeftInternalCoHomToObjectWithGivenLeftInternalCoHom</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X8197D69B805349AC">1.8 <span class="Heading">Coclosed Monoidal Categories</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X791BE0B0847A430D">1.8-1 InternalCoHomOnObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7FDF105D7F56EB53">1.8-2 InternalCoHomOnMorphisms</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X84DDA3DD878162B9">1.8-3 InternalCoHomOnMorphismsWithGivenInternalCoHoms</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X83CEC88D79AE5684">1.8-4 CoclosedMonoidalRightEvaluationMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X79333EC9822EA316">1.8-5 CoclosedMonoidalRightEvaluationMorphismWithGivenRange</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X80CA11547F3909E3">1.8-6 CoclosedMonoidalRightCoevaluationMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7F1C10897EC4D14E">1.8-7 CoclosedMonoidalRightCoevaluationMorphismWithGivenSource</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X82B0937678F04730">1.8-8 TensorProductToInternalCoHomRightAdjunctMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X833D7B567810D7F3">1.8-9 TensorProductToInternalCoHomRightAdjunctMorphismWithGivenInternalCoHom</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8623CC567D687FFD">1.8-10 InternalCoHomToTensorProductRightAdjunctMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X821B5212835BD1F6">1.8-11 InternalCoHomToTensorProductRightAdjunctMorphismWithGivenTensorProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X81020D9E85C3280A">1.8-12 CoclosedMonoidalLeftEvaluationMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7A1801D77EECEA29">1.8-13 CoclosedMonoidalLeftEvaluationMorphismWithGivenRange</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7D6905F582F06003">1.8-14 CoclosedMonoidalLeftCoevaluationMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X802A3FC48280FBDE">1.8-15 CoclosedMonoidalLeftCoevaluationMorphismWithGivenSource</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7FB4953B7F813D0B">1.8-16 TensorProductToInternalCoHomLeftAdjunctMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8312DB0A82A97D4B">1.8-17 TensorProductToInternalCoHomLeftAdjunctMorphismWithGivenInternalCoHom</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7A7FC1957A1905C6">1.8-18 InternalCoHomToTensorProductLeftAdjunctMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X85F970897F87BF2E">1.8-19 InternalCoHomToTensorProductLeftAdjunctMorphismWithGivenTensorProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8337DE6B7D61EAC2">1.8-20 MonoidalPreCoComposeMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X82A183B0807A0A01">1.8-21 MonoidalPreCoComposeMorphismWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X83FE0B8D853A76C1">1.8-22 MonoidalPostCoComposeMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X805DF38880B1E9E0">1.8-23 MonoidalPostCoComposeMorphismWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X817A1F7986256461">1.8-24 CoDualOnObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X840CBC837926138E">1.8-25 CoDualOnMorphisms</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X79750BFD824D2AAF">1.8-26 CoDualOnMorphismsWithGivenCoDuals</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7C65C05A788415E4">1.8-27 CoclosedEvaluationForCoDual</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7CAB615C86D97CE8">1.8-28 CoclosedEvaluationForCoDualWithGivenTensorProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7841B6757A510799">1.8-29 MorphismFromCoBidual</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7B2B002979E1CBF6">1.8-30 MorphismFromCoBidualWithGivenCoBidual</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7D9E57197C820E0E">1.8-31 InternalCoHomTensorProductCompatibilityMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X81E9DC8D7FCD361F">1.8-32 InternalCoHomTensorProductCompatibilityMorphismWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7B817BC97C1F1DF8">1.8-33 CoDualityTensorProductCompatibilityMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X82119ED686D3874C">1.8-34 CoDualityTensorProductCompatibilityMorphismWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7A4971267B80B14F">1.8-35 MorphismFromInternalCoHomToTensorProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7B60FB927C37E125">1.8-36 MorphismFromInternalCoHomToTensorProductWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X86C7E40C85318EFA">1.8-37 IsomorphismFromCoDualObjectToInternalCoHomFromTensorUnit</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X84C86E29800BB8BC">1.8-38 IsomorphismFromInternalCoHomFromTensorUnitToCoDualObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7AEE412D80799D09">1.8-39 UniversalPropertyOfCoDual</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X784CBFB984E66E7A">1.8-40 CoLambdaIntroduction</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X83520B098068CF62">1.8-41 CoLambdaElimination</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X83F11F6184DBD507">1.8-42 IsomorphismFromObjectToInternalCoHom</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8233C995828387E9">1.8-43 IsomorphismFromObjectToInternalCoHomWithGivenInternalCoHom</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X875A349280E2095C">1.8-44 IsomorphismFromInternalCoHomToObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X858AD1F986BA5BB2">1.8-45 IsomorphismFromInternalCoHomToObjectWithGivenInternalCoHom</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X849F4CB58466EAEB">1.9 <span class="Heading">Symmetric Closed Monoidal Categories</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X86F60BCA79C63F20">1.10 <span class="Heading">Symmetric Coclosed Monoidal Categories</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X805AEF9784062A31">1.11 <span class="Heading">Rigid Symmetric Closed Monoidal Categories</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X782B629D7E7835C9">1.11-1 IsomorphismFromTensorProductWithDualObjectToInternalHom</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X84D0668C7CA0B63D">1.11-2 IsomorphismFromInternalHomToTensorProductWithDualObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7D189B8280CECBA2">1.11-3 MorphismFromInternalHomToTensorProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7D10805D840AAC8D">1.11-4 MorphismFromInternalHomToTensorProductWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X85BA8C10817296F7">1.11-5 TensorProductInternalHomCompatibilityMorphismInverse</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7CCE67B281EF45C1">1.11-6 TensorProductInternalHomCompatibilityMorphismInverseWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X83849B327C8074E9">1.11-7 CoevaluationForDual</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7C65E6A97AAE0DE3">1.11-8 CoevaluationForDualWithGivenTensorProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X85D0C9487A22AFFE">1.11-9 TraceMap</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X82F0DBD485D93793">1.11-10 RankMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7E02E8197EA201EA">1.11-11 MorphismFromBidual</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X785CF0BB7BC0AC0D">1.11-12 MorphismFromBidualWithGivenBidual</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X79E86CAD853AB883">1.12 <span class="Heading">Rigid Symmetric Coclosed Monoidal Categories</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X82D4EF587F1C194C">1.12-1 IsomorphismFromInternalCoHomToTensorProductWithCoDualObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7FE736BA834D228A">1.12-2 IsomorphismFromTensorProductWithCoDualObjectToInternalCoHom</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7DCA54857A6B45DF">1.12-3 MorphismFromTensorProductToInternalCoHom</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7888F9947DDC15B5">1.12-4 MorphismFromTensorProductToInternalCoHomWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7E71AF0985C5AEC5">1.12-5 InternalCoHomTensorProductCompatibilityMorphismInverse</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X87BF8BE67AD5ABCF">1.12-6 InternalCoHomTensorProductCompatibilityMorphismInverseWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8695F9D97A8C6C61">1.12-7 CoclosedCoevaluationForCoDual</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X78B2703A7B81E340">1.12-8 CoclosedCoevaluationForCoDualWithGivenTensorProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X829BE5F97A656200">1.12-9 CoTraceMap</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7C5CC8F97D95AD43">1.12-10 CoRankMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X85BDB94D85C67725">1.12-11 MorphismToCoBidual</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X800035BF867418D0">1.12-12 MorphismToCoBidualWithGivenCoBidual</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X7B40ED8B78D067A5">1.13 <span class="Heading">Convenience Methods</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8055FF847AC2102A">1.13-1 InternalHom</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7CB6A9497A971F59">1.13-2 InternalCoHom</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X82DE5FDA794914A0">1.13-3 LeftInternalHom</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X862E6A787C9E1F92">1.13-4 LeftInternalCoHom</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X85C8C80F785AEB5E">1.14 <span class="Heading">Add-methods</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X78DA7EC37A1E0CCC">1.14-1 AddLeftDistributivityExpanding</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X814BA200802D26E4">1.14-2 AddLeftDistributivityExpandingWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8381C23A8264435B">1.14-3 AddLeftDistributivityFactoring</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7F0A439478576973">1.14-4 AddLeftDistributivityFactoringWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X82E93F8E79CB7338">1.14-5 AddRightDistributivityExpanding</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7A6178C17EFC817A">1.14-6 AddRightDistributivityExpandingWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X79B283777BC5F12C">1.14-7 AddRightDistributivityFactoring</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X842099557CF2036E">1.14-8 AddRightDistributivityFactoringWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7F9C3FD38397D9D4">1.14-9 AddBraiding</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8423AA1A862E9780">1.14-10 AddBraidingInverse</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X85C7E40583A5955F">1.14-11 AddBraidingInverseWithGivenTensorProducts</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7A52CBE8801D6B28">1.14-12 AddBraidingWithGivenTensorProducts</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7996A3A980BD5783">1.14-13 AddClosedMonoidalLeftCoevaluationMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7FD9DC1D870FB3D2">1.14-14 AddClosedMonoidalLeftCoevaluationMorphismWithGivenRange</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X82E0E46E7B374DA9">1.14-15 AddClosedMonoidalLeftEvaluationMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8742C27B7D30E543">1.14-16 AddClosedMonoidalLeftEvaluationMorphismWithGivenSource</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X870332B286200F2A">1.14-17 AddClosedMonoidalRightCoevaluationMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7A06D2CC79874E18">1.14-18 AddClosedMonoidalRightCoevaluationMorphismWithGivenRange</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X82FD88E87B30334F">1.14-19 AddClosedMonoidalRightEvaluationMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7ECDA3E47F267341">1.14-20 AddClosedMonoidalRightEvaluationMorphismWithGivenSource</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X800DFCF37CC10CCC">1.14-21 AddDualOnMorphisms</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X85DA12C581E673DE">1.14-22 AddDualOnMorphismsWithGivenDuals</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7BB4DD5381EBF082">1.14-23 AddDualOnObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7FF9C96186646B7C">1.14-24 AddEvaluationForDual</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7CB63A4E7E905CD4">1.14-25 AddEvaluationForDualWithGivenTensorProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X79A5E1EF7F091948">1.14-26 AddInternalHomOnMorphisms</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8070203E80388349">1.14-27 AddInternalHomOnMorphismsWithGivenInternalHoms</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7B74F8FD8348D590">1.14-28 AddInternalHomOnObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X87D40CEF8247DF33">1.14-29 AddInternalHomToTensorProductLeftAdjunctMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X82D3E7BD7DD67116">1.14-30 AddInternalHomToTensorProductLeftAdjunctMorphismWithGivenTensorProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7BBC91088476613F">1.14-31 AddInternalHomToTensorProductLeftAdjunctionIsomorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X789D0ED680E7D176">1.14-32 AddInternalHomToTensorProductLeftAdjunctionIsomorphismWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X84B3BDBF8294E790">1.14-33 AddInternalHomToTensorProductRightAdjunctMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X807104E57D50EEB9">1.14-34 AddInternalHomToTensorProductRightAdjunctMorphismWithGivenTensorProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8634234A855F18D5">1.14-35 AddInternalHomToTensorProductRightAdjunctionIsomorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7A3FED8E84CD4A02">1.14-36 AddInternalHomToTensorProductRightAdjunctionIsomorphismWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7983CB57783E6813">1.14-37 AddIsomorphismFromDualObjectToInternalHomIntoTensorUnit</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X84E4949886CB84C9">1.14-38 AddIsomorphismFromInternalHomIntoTensorUnitToDualObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7FA9FE2B85CE866D">1.14-39 AddIsomorphismFromInternalHomToObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7D6421147BF6651B">1.14-40 AddIsomorphismFromInternalHomToObjectWithGivenInternalHom</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X82538F687DE872DD">1.14-41 AddIsomorphismFromObjectToInternalHom</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X78ED7FCC83D091AB">1.14-42 AddIsomorphismFromObjectToInternalHomWithGivenInternalHom</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8406FBCD7EE968FF">1.14-43 AddLambdaElimination</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X84944B6283F2802A">1.14-44 AddLambdaIntroduction</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X843DC64486CB2ED1">1.14-45 AddMonoidalPostComposeMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7FC3725A7CF804F9">1.14-46 AddMonoidalPostComposeMorphismWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7B0C198782C01CBA">1.14-47 AddMonoidalPreComposeMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7A22CD657A2A338C">1.14-48 AddMonoidalPreComposeMorphismWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7CF664D87D8D5CA1">1.14-49 AddMorphismFromTensorProductToInternalHom</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X86D3AF4A80FA738D">1.14-50 AddMorphismFromTensorProductToInternalHomWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X864B98B08041EE6C">1.14-51 AddMorphismToBidual</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X84C05B087EFCE599">1.14-52 AddMorphismToBidualWithGivenBidual</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7A020DBF860317F5">1.14-53 AddTensorProductDualityCompatibilityMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X78D1B6AF8654A950">1.14-54 AddTensorProductDualityCompatibilityMorphismWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X83A6EF0B7ED71EED">1.14-55 AddTensorProductInternalHomCompatibilityMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X871C6B55843A0AF3">1.14-56 AddTensorProductInternalHomCompatibilityMorphismWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X817EAD878544BF68">1.14-57 AddTensorProductToInternalHomLeftAdjunctMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7B2FEF0985C2FACE">1.14-58 AddTensorProductToInternalHomLeftAdjunctMorphismWithGivenInternalHom</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X85A8D11983750164">1.14-59 AddTensorProductToInternalHomLeftAdjunctionIsomorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7AE873FD87E4B12D">1.14-60 AddTensorProductToInternalHomLeftAdjunctionIsomorphismWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7AF5FBEE859787CB">1.14-61 AddTensorProductToInternalHomRightAdjunctMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X86B3F2BF813AFBDA">1.14-62 AddTensorProductToInternalHomRightAdjunctMorphismWithGivenInternalHom</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X79777C5F825C788E">1.14-63 AddTensorProductToInternalHomRightAdjunctionIsomorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X86FD5F8A83CE2A59">1.14-64 AddTensorProductToInternalHomRightAdjunctionIsomorphismWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7FCEDB3B7DF69A1E">1.14-65 AddUniversalPropertyOfDual</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7D23088385F021AA">1.14-66 AddCoDualOnMorphisms</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7C2568FD82259231">1.14-67 AddCoDualOnMorphismsWithGivenCoDuals</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7C1CDE7F855ACB74">1.14-68 AddCoDualOnObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7D9B355D8261CB17">1.14-69 AddCoDualityTensorProductCompatibilityMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7CE8010980DBA597">1.14-70 AddCoDualityTensorProductCompatibilityMorphismWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7E7962CC7E809023">1.14-71 AddCoLambdaElimination</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7C3868657D8A0400">1.14-72 AddCoLambdaIntroduction</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X839204FD79F2968D">1.14-73 AddCoclosedEvaluationForCoDual</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X803976DB7C8F307C">1.14-74 AddCoclosedEvaluationForCoDualWithGivenTensorProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X829CAF887FAC5BF0">1.14-75 AddCoclosedMonoidalLeftCoevaluationMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7E7EBA4381366E7A">1.14-76 AddCoclosedMonoidalLeftCoevaluationMorphismWithGivenSource</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X81EC6B3E80876BC8">1.14-77 AddCoclosedMonoidalLeftEvaluationMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X839DE15C87358F99">1.14-78 AddCoclosedMonoidalLeftEvaluationMorphismWithGivenRange</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X78A8CB687ADC4653">1.14-79 AddCoclosedMonoidalRightCoevaluationMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X783C75CD79B2E8C9">1.14-80 AddCoclosedMonoidalRightCoevaluationMorphismWithGivenSource</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X85F82B2F84E55DD2">1.14-81 AddCoclosedMonoidalRightEvaluationMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X86DC2EF07B421CE0">1.14-82 AddCoclosedMonoidalRightEvaluationMorphismWithGivenRange</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7D63C4A57A467DAA">1.14-83 AddInternalCoHomOnMorphisms</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X87A67CDD86E0CE05">1.14-84 AddInternalCoHomOnMorphismsWithGivenInternalCoHoms</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X828648F183570AE3">1.14-85 AddInternalCoHomOnObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X78278696834ACA53">1.14-86 AddInternalCoHomTensorProductCompatibilityMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X82EA4C857C7BCC60">1.14-87 AddInternalCoHomTensorProductCompatibilityMorphismWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7C7256EE79374540">1.14-88 AddInternalCoHomToTensorProductLeftAdjunctMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X84EBD01D7843FAAD">1.14-89 AddInternalCoHomToTensorProductLeftAdjunctMorphismWithGivenTensorProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X858ED26087369677">1.14-90 AddInternalCoHomToTensorProductRightAdjunctMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7E97DAC0782AACEC">1.14-91 AddInternalCoHomToTensorProductRightAdjunctMorphismWithGivenTensorProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7A2B14497B4924A7">1.14-92 AddIsomorphismFromCoDualObjectToInternalCoHomFromTensorUnit</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8143326C7BE5E321">1.14-93 AddIsomorphismFromInternalCoHomFromTensorUnitToCoDualObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7C9F35A779395B26">1.14-94 AddIsomorphismFromInternalCoHomToObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7D0E88AC7C0304D3">1.14-95 AddIsomorphismFromInternalCoHomToObjectWithGivenInternalCoHom</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7E18F31C86620139">1.14-96 AddIsomorphismFromObjectToInternalCoHom</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8304276383585ECC">1.14-97 AddIsomorphismFromObjectToInternalCoHomWithGivenInternalCoHom</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7DE479077F155716">1.14-98 AddMonoidalPostCoComposeMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X79858B577BD4F1E1">1.14-99 AddMonoidalPostCoComposeMorphismWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7D1662EA819EA1A2">1.14-100 AddMonoidalPreCoComposeMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X81DFED7386A953E0">1.14-101 AddMonoidalPreCoComposeMorphismWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7D1615257BAA311F">1.14-102 AddMorphismFromCoBidual</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X84D1F74D8118B2A0">1.14-103 AddMorphismFromCoBidualWithGivenCoBidual</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7C3C01F1834A4B9B">1.14-104 AddMorphismFromInternalCoHomToTensorProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X87AB2C4D84F19F37">1.14-105 AddMorphismFromInternalCoHomToTensorProductWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7C0E0CF87FEFEB0D">1.14-106 AddTensorProductToInternalCoHomLeftAdjunctMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7A838651781657DA">1.14-107 AddTensorProductToInternalCoHomLeftAdjunctMorphismWithGivenInternalCoHom</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8123546E81EE383A">1.14-108 AddTensorProductToInternalCoHomRightAdjunctMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8698898584E99695">1.14-109 AddTensorProductToInternalCoHomRightAdjunctMorphismWithGivenInternalCoHom</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8519ECF17EC07916">1.14-110 AddUniversalPropertyOfCoDual</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7F868E597F1C1AD7">1.14-111 AddIsomorphismFromLeftDualObjectToLeftInternalHomIntoTensorUnit</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X810B50C27901021C">1.14-112 AddIsomorphismFromLeftInternalHomIntoTensorUnitToLeftDualObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X87415032853E8340">1.14-113 AddIsomorphismFromLeftInternalHomToObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X83DAADEE8139DACA">1.14-114 AddIsomorphismFromLeftInternalHomToObjectWithGivenLeftInternalHom</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7FA337D07BCD9D5B">1.14-115 AddIsomorphismFromObjectToLeftInternalHom</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7EA7B1777FCAC4D1">1.14-116 AddIsomorphismFromObjectToLeftInternalHomWithGivenLeftInternalHom</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7D1E4F66851991AB">1.14-117 AddLeftClosedMonoidalCoevaluationMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7EF0D5B782AB75FA">1.14-118 AddLeftClosedMonoidalCoevaluationMorphismWithGivenRange</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7FD8142C7CBF7FB1">1.14-119 AddLeftClosedMonoidalEvaluationForLeftDual</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7A89130185CCF31D">1.14-120 AddLeftClosedMonoidalEvaluationForLeftDualWithGivenTensorProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7D75530C7E938B81">1.14-121 AddLeftClosedMonoidalEvaluationMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8535FD8E7894236B">1.14-122 AddLeftClosedMonoidalEvaluationMorphismWithGivenSource</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X869B3FD87FC09E21">1.14-123 AddLeftClosedMonoidalLambdaElimination</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7CC085AB7DBC581A">1.14-124 AddLeftClosedMonoidalLambdaIntroduction</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7BE971CB7E989544">1.14-125 AddLeftClosedMonoidalPostComposeMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7B6DBF17796A971A">1.14-126 AddLeftClosedMonoidalPostComposeMorphismWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X799401467830D201">1.14-127 AddLeftClosedMonoidalPreComposeMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7915D4437C9257A5">1.14-128 AddLeftClosedMonoidalPreComposeMorphismWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X79D85C017917C1D4">1.14-129 AddLeftDualOnMorphisms</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X816C625A82BCDDE3">1.14-130 AddLeftDualOnMorphismsWithGivenLeftDuals</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7CB93B6E8555359D">1.14-131 AddLeftDualOnObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X79B3B2F586530EFF">1.14-132 AddLeftInternalHomOnMorphisms</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7DDC722B78B659A2">1.14-133 AddLeftInternalHomOnMorphismsWithGivenLeftInternalHoms</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7FCF9DEA7F6B73F9">1.14-134 AddLeftInternalHomOnObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7F5EAC1E8104166E">1.14-135 AddLeftInternalHomToTensorProductAdjunctMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7C437ED77E95B84B">1.14-136 AddLeftInternalHomToTensorProductAdjunctMorphismWithGivenTensorProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7CA082FF7B01D8FB">1.14-137 AddMorphismFromTensorProductToLeftInternalHom</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8028DDA77A2AF1D0">1.14-138 AddMorphismFromTensorProductToLeftInternalHomWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X80EC71197C2C11D1">1.14-139 AddMorphismToLeftBidual</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X869265BC78942371">1.14-140 AddMorphismToLeftBidualWithGivenLeftBidual</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7953DC1F805D8C1A">1.14-141 AddTensorProductLeftDualityCompatibilityMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X836F9F347AB09804">1.14-142 AddTensorProductLeftDualityCompatibilityMorphismWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7A76B21F7DD29DD4">1.14-143 AddTensorProductLeftInternalHomCompatibilityMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X78BE6DC079995BE8">1.14-144 AddTensorProductLeftInternalHomCompatibilityMorphismWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7A7B64B17E0CB68F">1.14-145 AddTensorProductToLeftInternalHomAdjunctMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X852D330679DA479F">1.14-146 AddTensorProductToLeftInternalHomAdjunctMorphismWithGivenLeftInternalHom</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X814F44BD7ED47029">1.14-147 AddUniversalPropertyOfLeftDual</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7DF0FCAF7EF18F8F">1.14-148 AddIsomorphismFromLeftCoDualObjectToLeftInternalCoHomFromTensorUnit</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X85BAFAF48192ADFD">1.14-149 AddIsomorphismFromLeftInternalCoHomFromTensorUnitToLeftCoDualObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7F13CA18790E4170">1.14-150 AddIsomorphismFromLeftInternalCoHomToObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8695E6B0854AC59F">1.14-151 AddIsomorphismFromLeftInternalCoHomToObjectWithGivenLeftInternalCoHom</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X78B4B7FE82DC4548">1.14-152 AddIsomorphismFromObjectToLeftInternalCoHom</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8569A8107E98C1A7">1.14-153 AddIsomorphismFromObjectToLeftInternalCoHomWithGivenLeftInternalCoHom</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X834FFF597E5AD96E">1.14-154 AddLeftCoDualOnMorphisms</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7EFAFD687AE8B744">1.14-155 AddLeftCoDualOnMorphismsWithGivenLeftCoDuals</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X85C97E8D7982AA91">1.14-156 AddLeftCoDualOnObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X859C18CA80B931C8">1.14-157 AddLeftCoDualityTensorProductCompatibilityMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7D8D0BE17F8837FB">1.14-158 AddLeftCoDualityTensorProductCompatibilityMorphismWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X788B63417F1F60F9">1.14-159 AddLeftCoclosedMonoidalCoevaluationMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X82B5F67881855573">1.14-160 AddLeftCoclosedMonoidalCoevaluationMorphismWithGivenSource</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7825101881671E7F">1.14-161 AddLeftCoclosedMonoidalEvaluationForLeftCoDual</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X846EE69A797450F9">1.14-162 AddLeftCoclosedMonoidalEvaluationForLeftCoDualWithGivenTensorProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X826AE548803450C1">1.14-163 AddLeftCoclosedMonoidalEvaluationMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8082909C8786B490">1.14-164 AddLeftCoclosedMonoidalEvaluationMorphismWithGivenRange</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X84635F4580F63BD0">1.14-165 AddLeftCoclosedMonoidalLambdaElimination</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X83DF33EF7A19E291">1.14-166 AddLeftCoclosedMonoidalLambdaIntroduction</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7954E35E784BCB8B">1.14-167 AddLeftCoclosedMonoidalPostCoComposeMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7FE2EC92781C752E">1.14-168 AddLeftCoclosedMonoidalPostCoComposeMorphismWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7DC17F0884BAD720">1.14-169 AddLeftCoclosedMonoidalPreCoComposeMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X86DB94FE8301038C">1.14-170 AddLeftCoclosedMonoidalPreCoComposeMorphismWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X829E5F7E783539C3">1.14-171 AddLeftInternalCoHomOnMorphisms</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X78538C8E78635666">1.14-172 AddLeftInternalCoHomOnMorphismsWithGivenLeftInternalCoHoms</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X82901BEB81D0A428">1.14-173 AddLeftInternalCoHomOnObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X814CCC847F369708">1.14-174 AddLeftInternalCoHomTensorProductCompatibilityMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7C3A3DEB7BA72741">1.14-175 AddLeftInternalCoHomTensorProductCompatibilityMorphismWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X80C1A62B812B4565">1.14-176 AddLeftInternalCoHomToTensorProductAdjunctMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X83DDE598805FFA88">1.14-177 AddLeftInternalCoHomToTensorProductAdjunctMorphismWithGivenTensorProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8104426A8327EF5E">1.14-178 AddMorphismFromLeftCoBidual</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X849C36147F09B8A0">1.14-179 AddMorphismFromLeftCoBidualWithGivenLeftCoBidual</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X86168FF07A697A15">1.14-180 AddMorphismFromLeftInternalCoHomToTensorProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X830428C27A6BC07B">1.14-181 AddMorphismFromLeftInternalCoHomToTensorProductWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7AA7EDE881098270">1.14-182 AddTensorProductToLeftInternalCoHomAdjunctMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7CDB23877B3C8292">1.14-183 AddTensorProductToLeftInternalCoHomAdjunctMorphismWithGivenLeftInternalCoHom</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X864F1EF47CAD2BE8">1.14-184 AddUniversalPropertyOfLeftCoDual</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X79CDE3B87D14EF9A">1.14-185 AddAssociatorLeftToRight</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X850B5B357F592FAE">1.14-186 AddAssociatorLeftToRightWithGivenTensorProducts</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8045C4FC7B4912B4">1.14-187 AddAssociatorRightToLeft</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7CF105217904D280">1.14-188 AddAssociatorRightToLeftWithGivenTensorProducts</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7986052487D3CDBB">1.14-189 AddLeftUnitor</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X793D2C657F19096D">1.14-190 AddLeftUnitorInverse</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X87CB487587ED3EC5">1.14-191 AddLeftUnitorInverseWithGivenTensorProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8614FD9C78812C98">1.14-192 AddLeftUnitorWithGivenTensorProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8568708E7C5D8D28">1.14-193 AddRightUnitor</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7B2AAD6286833F68">1.14-194 AddRightUnitorInverse</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8682171F86C6793E">1.14-195 AddRightUnitorInverseWithGivenTensorProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7DB39DC9794F3FCA">1.14-196 AddRightUnitorWithGivenTensorProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X83DEDFA3803035BC">1.14-197 AddTensorProductOnMorphisms</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X879659397D11AD9F">1.14-198 AddTensorProductOnMorphismsWithGivenTensorProducts</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7CED389B792142F5">1.14-199 AddTensorProductOnObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7BC4B940858F903B">1.14-200 AddTensorUnit</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8586506084917A30">1.14-201 AddCoevaluationForDual</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X831DC3947941E8BA">1.14-202 AddCoevaluationForDualWithGivenTensorProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X817D08298188F2BC">1.14-203 AddIsomorphismFromInternalHomToTensorProductWithDualObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X840BC8AB7DFFD68E">1.14-204 AddIsomorphismFromTensorProductWithDualObjectToInternalHom</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7D2FDE687E0CB66A">1.14-205 AddMorphismFromBidual</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X877C409E865C2BB3">1.14-206 AddMorphismFromBidualWithGivenBidual</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X82FDEF277A71FABF">1.14-207 AddMorphismFromInternalHomToTensorProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7A4A4C668706D593">1.14-208 AddMorphismFromInternalHomToTensorProductWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X849B17E08679450A">1.14-209 AddRankMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X798FA16B818559DB">1.14-210 AddTensorProductInternalHomCompatibilityMorphismInverse</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7D9EA11980170B0C">1.14-211 AddTensorProductInternalHomCompatibilityMorphismInverseWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8446431880FFF111">1.14-212 AddTraceMap</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7A3D91F87F170676">1.14-213 AddCoRankMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7AA8757780D75E1F">1.14-214 AddCoTraceMap</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X82087A8C7E5EBAA8">1.14-215 AddCoclosedCoevaluationForCoDual</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X813CF5C07BAFD19C">1.14-216 AddCoclosedCoevaluationForCoDualWithGivenTensorProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7CA7972381FC507F">1.14-217 AddInternalCoHomTensorProductCompatibilityMorphismInverse</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X82F222EC80852CF1">1.14-218 AddInternalCoHomTensorProductCompatibilityMorphismInverseWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X84E2048279A169A6">1.14-219 AddIsomorphismFromInternalCoHomToTensorProductWithCoDualObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7DFE79B48125A1E0">1.14-220 AddIsomorphismFromTensorProductWithCoDualObjectToInternalCoHom</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7F27D275849C84B2">1.14-221 AddMorphismFromTensorProductToInternalCoHom</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7B5706318327501E">1.14-222 AddMorphismFromTensorProductToInternalCoHomWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7EBD7033871B0F3D">1.14-223 AddMorphismToCoBidual</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X867E02E07CEC5B34">1.14-224 AddMorphismToCoBidualWithGivenCoBidual</a></span>
</div></div>
</div>

<h3>1 <span class="Heading">Monoidal Categories</span></h3>

<p><a id="X808DC49C7ED99B52" name="X808DC49C7ED99B52"></a></p>

<h4>1.1 <span class="Heading">Monoidal Categories</span></h4>

<p>A <span class="Math">6</span>-tuple <span class="Math">( \mathbf{C}, \otimes, 1, \alpha, \lambda, \rho )</span> consisting of</p>


<ul>
<li><p>a category <span class="Math">\mathbf{C}</span>,</p>

</li>
<li><p>a functor <span class="Math">\otimes: \mathbf{C} \times \mathbf{C} \rightarrow \mathbf{C}</span> compatible with the congruence of morphisms,</p>

</li>
<li><p>an object <span class="Math">1 \in \mathbf{C}</span>,</p>

</li>
<li><p>a natural isomorphism <span class="Math">\alpha_{a,b,c}: a \otimes (b \otimes c) \cong (a \otimes b) \otimes c</span>,</p>

</li>
<li><p>a natural isomorphism <span class="Math">\lambda_{a}: 1 \otimes a \cong a</span>,</p>

</li>
<li><p>a natural isomorphism <span class="Math">\rho_{a}: a \otimes 1 \cong a</span>,</p>

</li>
</ul>
<p>is called a <em>monoidal category</em>, if</p>


<ul>
<li><p>for all objects <span class="Math">a,b,c,d</span>, the pentagon identity holds:</p>

</li>
</ul>
<p><span class="Math">(\alpha_{a,b,c} \otimes \mathrm{id}_d) \circ \alpha_{a,b \otimes c, d} \circ ( \mathrm{id}_a \otimes \alpha_{b,c,d} ) \sim \alpha_{a \otimes b, c, d} \circ \alpha_{a,b,c \otimes d}</span>,</p>


<ul>
<li><p>for all objects <span class="Math">a,c</span>, the triangle identity holds:</p>

</li>
</ul>
<p><span class="Math">( \rho_a \otimes \mathrm{id}_c ) \circ \alpha_{a,1,c} \sim \mathrm{id}_a \otimes \lambda_c</span>.</p>

<p>The corresponding GAP property is given by <code class="code">IsMonoidalCategory</code>.</p>

<p><a id="X84997A1E8188D6BE" name="X84997A1E8188D6BE"></a></p>

<h5>1.1-1 TensorProductOnMorphisms</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TensorProductOnMorphisms</code>( <var class="Arg">alpha</var>, <var class="Arg">beta</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(a \otimes b, a' \otimes b')</span></p>

<p>The arguments are two morphisms <span class="Math">\alpha: a \rightarrow a', \beta: b \rightarrow b'</span>. The output is the tensor product <span class="Math">\alpha \otimes \beta</span>.</p>

<p><a id="X85008BF07C2C0386" name="X85008BF07C2C0386"></a></p>

<h5>1.1-2 TensorProductOnMorphismsWithGivenTensorProducts</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TensorProductOnMorphismsWithGivenTensorProducts</code>( <var class="Arg">s</var>, <var class="Arg">alpha</var>, <var class="Arg">beta</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(a \otimes b, a' \otimes b')</span></p>

<p>The arguments are an object <span class="Math">s = a \otimes b</span>, two morphisms <span class="Math">\alpha: a \rightarrow a', \beta: b \rightarrow b'</span>, and an object <span class="Math">r = a' \otimes b'</span>. The output is the tensor product <span class="Math">\alpha \otimes \beta</span>.</p>

<p><a id="X84C2FAEA7B9678AA" name="X84C2FAEA7B9678AA"></a></p>

<h5>1.1-3 AssociatorRightToLeft</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AssociatorRightToLeft</code>( <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">c</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( a \otimes (b \otimes c), (a \otimes b) \otimes c )</span>.</p>

<p>The arguments are three objects <span class="Math">a,b,c</span>. The output is the associator <span class="Math">\alpha_{a,(b,c)}: a \otimes (b \otimes c) \rightarrow (a \otimes b) \otimes c</span>.</p>

<p><a id="X85645C4D86060ED2" name="X85645C4D86060ED2"></a></p>

<h5>1.1-4 AssociatorRightToLeftWithGivenTensorProducts</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AssociatorRightToLeftWithGivenTensorProducts</code>( <var class="Arg">s</var>, <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">c</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( a \otimes (b \otimes c), (a \otimes b) \otimes c )</span>.</p>

<p>The arguments are an object <span class="Math">s = a \otimes (b \otimes c)</span>, three objects <span class="Math">a,b,c</span>, and an object <span class="Math">r = (a \otimes b) \otimes c</span>. The output is the associator <span class="Math">\alpha_{a,(b,c)}: a \otimes (b \otimes c) \rightarrow (a \otimes b) \otimes c</span>.</p>

<p><a id="X7C5A064C7E1995F1" name="X7C5A064C7E1995F1"></a></p>

<h5>1.1-5 AssociatorLeftToRight</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AssociatorLeftToRight</code>( <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">c</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( (a \otimes b) \otimes c \rightarrow a \otimes (b \otimes c) )</span>.</p>

<p>The arguments are three objects <span class="Math">a,b,c</span>. The output is the associator <span class="Math">\alpha_{(a,b),c}: (a \otimes b) \otimes c \rightarrow a \otimes (b \otimes c)</span>.</p>

<p><a id="X7C59D73F8389E389" name="X7C59D73F8389E389"></a></p>

<h5>1.1-6 AssociatorLeftToRightWithGivenTensorProducts</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AssociatorLeftToRightWithGivenTensorProducts</code>( <var class="Arg">s</var>, <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">c</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( (a \otimes b) \otimes c \rightarrow a \otimes (b \otimes c) )</span>.</p>

<p>The arguments are an object <span class="Math">s = (a \otimes b) \otimes c</span>, three objects <span class="Math">a,b,c</span>, and an object <span class="Math">r = a \otimes (b \otimes c)</span>. The output is the associator <span class="Math">\alpha_{(a,b),c}: (a \otimes b) \otimes c \rightarrow a \otimes (b \otimes c)</span>.</p>

<p><a id="X7EBCAFDD81BDB655" name="X7EBCAFDD81BDB655"></a></p>

<h5>1.1-7 LeftUnitor</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftUnitor</code>( <var class="Arg">a</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(1 \otimes a, a)</span></p>

<p>The argument is an object <span class="Math">a</span>. The output is the left unitor <span class="Math">\lambda_a: 1 \otimes a \rightarrow a</span>.</p>

<p><a id="X7ED284DF7BA21774" name="X7ED284DF7BA21774"></a></p>

<h5>1.1-8 LeftUnitorWithGivenTensorProduct</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftUnitorWithGivenTensorProduct</code>( <var class="Arg">a</var>, <var class="Arg">s</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(1 \otimes a, a)</span></p>

<p>The arguments are an object <span class="Math">a</span> and an object <span class="Math">s = 1 \otimes a</span>. The output is the left unitor <span class="Math">\lambda_a: 1 \otimes a \rightarrow a</span>.</p>

<p><a id="X79A274078147A9F7" name="X79A274078147A9F7"></a></p>

<h5>1.1-9 LeftUnitorInverse</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftUnitorInverse</code>( <var class="Arg">a</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(a, 1 \otimes a)</span></p>

<p>The argument is an object <span class="Math">a</span>. The output is the inverse of the left unitor <span class="Math">\lambda_a^{-1}: a \rightarrow 1 \otimes a</span>.</p>

<p><a id="X849609447CAE996B" name="X849609447CAE996B"></a></p>

<h5>1.1-10 LeftUnitorInverseWithGivenTensorProduct</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftUnitorInverseWithGivenTensorProduct</code>( <var class="Arg">a</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(a, 1 \otimes a)</span></p>

<p>The argument is an object <span class="Math">a</span> and an object <span class="Math">r = 1 \otimes a</span>. The output is the inverse of the left unitor <span class="Math">\lambda_a^{-1}: a \rightarrow 1 \otimes a</span>.</p>

<p><a id="X82F758CB7A23468A" name="X82F758CB7A23468A"></a></p>

<h5>1.1-11 RightUnitor</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ RightUnitor</code>( <var class="Arg">a</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(a \otimes 1, a)</span></p>

<p>The argument is an object <span class="Math">a</span>. The output is the right unitor <span class="Math">\rho_a: a \otimes 1 \rightarrow a</span>.</p>

<p><a id="X84C8F97F7BF2282D" name="X84C8F97F7BF2282D"></a></p>

<h5>1.1-12 RightUnitorWithGivenTensorProduct</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ RightUnitorWithGivenTensorProduct</code>( <var class="Arg">a</var>, <var class="Arg">s</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(a \otimes 1, a)</span></p>

<p>The arguments are an object <span class="Math">a</span> and an object <span class="Math">s = a \otimes 1</span>. The output is the right unitor <span class="Math">\rho_a: a \otimes 1 \rightarrow a</span>.</p>

<p><a id="X82DC825480E87301" name="X82DC825480E87301"></a></p>

<h5>1.1-13 RightUnitorInverse</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ RightUnitorInverse</code>( <var class="Arg">a</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(a, a \otimes 1)</span></p>

<p>The argument is an object <span class="Math">a</span>. The output is the inverse of the right unitor <span class="Math">\rho_a^{-1}: a \rightarrow a \otimes 1</span>.</p>

<p><a id="X85A8A87C87B33008" name="X85A8A87C87B33008"></a></p>

<h5>1.1-14 RightUnitorInverseWithGivenTensorProduct</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ RightUnitorInverseWithGivenTensorProduct</code>( <var class="Arg">a</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(a, a \otimes 1)</span></p>

<p>The arguments are an object <span class="Math">a</span> and an object <span class="Math">r = a \otimes 1</span>. The output is the inverse of the right unitor <span class="Math">\rho_a^{-1}: a \rightarrow a \otimes 1</span>.</p>

<p><a id="X797034F17AA47EE0" name="X797034F17AA47EE0"></a></p>

<h5>1.1-15 TensorProductOnObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TensorProductOnObjects</code>( <var class="Arg">a</var>, <var class="Arg">b</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: an object</p>

<p>The arguments are two objects <span class="Math">a, b</span>. The output is the tensor product <span class="Math">a \otimes b</span>.</p>

<p><a id="X7BF7FFDF8789474A" name="X7BF7FFDF8789474A"></a></p>

<h5>1.1-16 TensorUnit</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TensorUnit</code>( <var class="Arg">C</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: an object</p>

<p>The argument is a category <span class="Math">\mathbf{C}</span>. The output is the tensor unit <span class="Math">1</span> of <span class="Math">\mathbf{C}</span>.</p>

<p><a id="X7FB8551A815BEC53" name="X7FB8551A815BEC53"></a></p>

<h4>1.2 <span class="Heading">Additive Monoidal Categories</span></h4>

<p><a id="X7ACF268E7D82B0C9" name="X7ACF268E7D82B0C9"></a></p>

<h5>1.2-1 LeftDistributivityExpanding</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftDistributivityExpanding</code>( <var class="Arg">a</var>, <var class="Arg">L</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( a \otimes (b_1 \oplus \dots \oplus b_n), (a \otimes b_1) \oplus \dots \oplus (a \otimes b_n) )</span></p>

<p>The arguments are an object <span class="Math">a</span> and a list of objects <span class="Math">L = (b_1, \dots, b_n)</span>. The output is the left distributivity morphism <span class="Math">a \otimes (b_1 \oplus \dots \oplus b_n) \rightarrow (a \otimes b_1) \oplus \dots \oplus (a \otimes b_n)</span>.</p>

<p><a id="X7CA18968862D2285" name="X7CA18968862D2285"></a></p>

<h5>1.2-2 LeftDistributivityExpandingWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftDistributivityExpandingWithGivenObjects</code>( <var class="Arg">s</var>, <var class="Arg">a</var>, <var class="Arg">L</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( s, r )</span></p>

<p>The arguments are an object <span class="Math">s = a \otimes (b_1 \oplus \dots \oplus b_n)</span>, an object <span class="Math">a</span>, a list of objects <span class="Math">L = (b_1, \dots, b_n)</span>, and an object <span class="Math">r = (a \otimes b_1) \oplus \dots \oplus (a \otimes b_n)</span>. The output is the left distributivity morphism <span class="Math">s \rightarrow r</span>.</p>

<p><a id="X780322FE7E5A626D" name="X780322FE7E5A626D"></a></p>

<h5>1.2-3 LeftDistributivityFactoring</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftDistributivityFactoring</code>( <var class="Arg">a</var>, <var class="Arg">L</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( (a \otimes b_1) \oplus \dots \oplus (a \otimes b_n), a \otimes (b_1 \oplus \dots \oplus b_n) )</span></p>

<p>The arguments are an object <span class="Math">a</span> and a list of objects <span class="Math">L = (b_1, \dots, b_n)</span>. The output is the left distributivity morphism <span class="Math">(a \otimes b_1) \oplus \dots \oplus (a \otimes b_n) \rightarrow a \otimes (b_1 \oplus \dots \oplus b_n)</span>.</p>

<p><a id="X784D8CD685F5F021" name="X784D8CD685F5F021"></a></p>

<h5>1.2-4 LeftDistributivityFactoringWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftDistributivityFactoringWithGivenObjects</code>( <var class="Arg">s</var>, <var class="Arg">a</var>, <var class="Arg">L</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( s, r )</span></p>

<p>The arguments are an object <span class="Math">s = (a \otimes b_1) \oplus \dots \oplus (a \otimes b_n)</span>, an object <span class="Math">a</span>, a list of objects <span class="Math">L = (b_1, \dots, b_n)</span>, and an object <span class="Math">r = a \otimes (b_1 \oplus \dots \oplus b_n)</span>. The output is the left distributivity morphism <span class="Math">s \rightarrow r</span>.</p>

<p><a id="X8409C74778A4313A" name="X8409C74778A4313A"></a></p>

<h5>1.2-5 RightDistributivityExpanding</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ RightDistributivityExpanding</code>( <var class="Arg">L</var>, <var class="Arg">a</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( (b_1 \oplus \dots \oplus b_n) \otimes a, (b_1 \otimes a) \oplus \dots \oplus (b_n \otimes a) )</span></p>

<p>The arguments are a list of objects <span class="Math">L = (b_1, \dots, b_n)</span> and an object <span class="Math">a</span>. The output is the right distributivity morphism <span class="Math">(b_1 \oplus \dots \oplus b_n) \otimes a \rightarrow (b_1 \otimes a) \oplus \dots \oplus (b_n \otimes a)</span>.</p>

<p><a id="X7DBE629F811DEADC" name="X7DBE629F811DEADC"></a></p>

<h5>1.2-6 RightDistributivityExpandingWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ RightDistributivityExpandingWithGivenObjects</code>( <var class="Arg">s</var>, <var class="Arg">L</var>, <var class="Arg">a</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( s, r )</span></p>

<p>The arguments are an object <span class="Math">s = (b_1 \oplus \dots \oplus b_n) \otimes a</span>, a list of objects <span class="Math">L = (b_1, \dots, b_n)</span>, an object <span class="Math">a</span>, and an object <span class="Math">r = (b_1 \otimes a) \oplus \dots \oplus (b_n \otimes a)</span>. The output is the right distributivity morphism <span class="Math">s \rightarrow r</span>.</p>

<p><a id="X86C5C33786C1DC28" name="X86C5C33786C1DC28"></a></p>

<h5>1.2-7 RightDistributivityFactoring</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ RightDistributivityFactoring</code>( <var class="Arg">L</var>, <var class="Arg">a</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( (b_1 \otimes a) \oplus \dots \oplus (b_n \otimes a), (b_1 \oplus \dots \oplus b_n) \otimes a)</span></p>

<p>The arguments are a list of objects <span class="Math">L = (b_1, \dots, b_n)</span> and an object <span class="Math">a</span>. The output is the right distributivity morphism <span class="Math">(b_1 \otimes a) \oplus \dots \oplus (b_n \otimes a) \rightarrow (b_1 \oplus \dots \oplus b_n) \otimes a </span>.</p>

<p><a id="X795267217F7807CE" name="X795267217F7807CE"></a></p>

<h5>1.2-8 RightDistributivityFactoringWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ RightDistributivityFactoringWithGivenObjects</code>( <var class="Arg">s</var>, <var class="Arg">L</var>, <var class="Arg">a</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( s, r )</span></p>

<p>The arguments are an object <span class="Math">s = (b_1 \otimes a) \oplus \dots \oplus (b_n \otimes a)</span>, a list of objects <span class="Math">L = (b_1, \dots, b_n)</span>, an object <span class="Math">a</span>, and an object <span class="Math">r = (b_1 \oplus \dots \oplus b_n) \otimes a</span>. The output is the right distributivity morphism <span class="Math">s \rightarrow r</span>.</p>

<p><a id="X7D94AD967E6D60F1" name="X7D94AD967E6D60F1"></a></p>

<h4>1.3 <span class="Heading">Braided Monoidal Categories</span></h4>

<p>A monoidal category <span class="Math">\mathbf{C}</span> equipped with a natural isomorphism <span class="Math">B_{a,b}: a \otimes b \cong b \otimes a</span> is called a <em>braided monoidal category</em> if</p>


<ul>
<li><p><span class="Math">\lambda_a \circ B_{a,1} \sim \rho_a</span>,</p>

</li>
<li><p><span class="Math">(B_{c,a} \otimes \mathrm{id}_b) \circ \alpha_{c,a,b} \circ B_{a \otimes b,c} \sim \alpha_{a,c,b} \circ ( \mathrm{id}_a \otimes B_{b,c}) \circ \alpha^{-1}_{a,b,c}</span>,</p>

</li>
<li><p><span class="Math">( \mathrm{id}_b \otimes B_{c,a} ) \circ \alpha^{-1}_{b,c,a} \circ B_{a,b \otimes c} \sim \alpha^{-1}_{b,a,c} \circ (B_{a,b} \otimes \mathrm{id}_c) \circ \alpha_{a,b,c}</span>.</p>

</li>
</ul>
<p>The corresponding GAP property is given by <code class="code">IsBraidedMonoidalCategory</code>.</p>

<p><a id="X7C6ADBFE7A8DD1E3" name="X7C6ADBFE7A8DD1E3"></a></p>

<h5>1.3-1 Braiding</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ Braiding</code>( <var class="Arg">a</var>, <var class="Arg">b</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( a \otimes b, b \otimes a )</span>.</p>

<p>The arguments are two objects <span class="Math">a,b</span>. The output is the braiding <span class="Math"> B_{a,b}: a \otimes b \rightarrow b \otimes a</span>.</p>

<p><a id="X7F4B09A87B2500C0" name="X7F4B09A87B2500C0"></a></p>

<h5>1.3-2 BraidingWithGivenTensorProducts</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ BraidingWithGivenTensorProducts</code>( <var class="Arg">s</var>, <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( a \otimes b, b \otimes a )</span>.</p>

<p>The arguments are an object <span class="Math">s = a \otimes b</span>, two objects <span class="Math">a,b</span>, and an object <span class="Math">r = b \otimes a</span>. The output is the braiding <span class="Math"> B_{a,b}: a \otimes b \rightarrow b \otimes a</span>.</p>

<p><a id="X8195EC5279D3E8D0" name="X8195EC5279D3E8D0"></a></p>

<h5>1.3-3 BraidingInverse</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ BraidingInverse</code>( <var class="Arg">a</var>, <var class="Arg">b</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( b \otimes a, a \otimes b )</span>.</p>

<p>The arguments are two objects <span class="Math">a,b</span>. The output is the inverse braiding <span class="Math"> B_{a,b}^{-1}: b \otimes a \rightarrow a \otimes b</span>.</p>

<p><a id="X854AFBC67C836769" name="X854AFBC67C836769"></a></p>

<h5>1.3-4 BraidingInverseWithGivenTensorProducts</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ BraidingInverseWithGivenTensorProducts</code>( <var class="Arg">s</var>, <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( b \otimes a, a \otimes b )</span>.</p>

<p>The arguments are an object <span class="Math">s = b \otimes a</span>, two objects <span class="Math">a,b</span>, and an object <span class="Math">r = a \otimes b</span>. The output is the inverse braiding <span class="Math"> B_{a,b}^{-1}: b \otimes a \rightarrow a \otimes b</span>.</p>

<p><a id="X85ED71067F7CEA82" name="X85ED71067F7CEA82"></a></p>

<h4>1.4 <span class="Heading">Symmetric Monoidal Categories</span></h4>

<p>A braided monoidal category <span class="Math">\mathbf{C}</span> is called <em>symmetric monoidal category</em> if <span class="Math">B_{a,b}^{-1} \sim B_{b,a}</span>. The corresponding GAP property is given by <code class="code">IsSymmetricMonoidalCategory</code>.</p>

<p><a id="X85035E9683B050D0" name="X85035E9683B050D0"></a></p>

<h4>1.5 <span class="Heading">Left Closed Monoidal Categories</span></h4>

<p>A monoidal category <span class="Math">\mathbf{C}</span> which has for each functor <span class="Math">- \otimes b: \mathbf{C} \rightarrow \mathbf{C}</span> a right adjoint (denoted by <span class="Math">\mathrm{\underline{Hom}_\ell}(b,-)</span>) is called a <em>left closed monoidal category</em>.</p>

<p>If no operations involving left duals are installed manually, the left dual objects will be derived as <span class="Math">a^\vee \coloneqq \mathrm{\underline{Hom}_\ell}(a,1)</span>.</p>

<p>The corresponding GAP property is called <code class="code">IsLeftClosedMonoidalCategory</code>.</p>

<p><a id="X87A4C0637EB8A18E" name="X87A4C0637EB8A18E"></a></p>

<h5>1.5-1 LeftInternalHomOnObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftInternalHomOnObjects</code>( <var class="Arg">a</var>, <var class="Arg">b</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: an object</p>

<p>The arguments are two objects <span class="Math">a,b</span>. The output is the internal hom object <span class="Math">\mathrm{\underline{Hom}_\ell}(a,b)</span>.</p>

<p><a id="X8439FF407D2C9C6E" name="X8439FF407D2C9C6E"></a></p>

<h5>1.5-2 LeftInternalHomOnMorphisms</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftInternalHomOnMorphisms</code>( <var class="Arg">alpha</var>, <var class="Arg">beta</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( \mathrm{\underline{Hom}_\ell}(a',b), \mathrm{\underline{Hom}_\ell}(a,b') )</span></p>

<p>The arguments are two morphisms <span class="Math">\alpha: a \rightarrow a', \beta: b \rightarrow b'</span>. The output is the internal hom morphism <span class="Math">\mathrm{\underline{Hom}_\ell}(\alpha,\beta): \mathrm{\underline{Hom}_\ell}(a',b) \rightarrow \mathrm{\underline{Hom}_\ell}(a,b')</span>.</p>

<p><a id="X7861C2AD82F62C77" name="X7861C2AD82F62C77"></a></p>

<h5>1.5-3 LeftInternalHomOnMorphismsWithGivenLeftInternalHoms</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftInternalHomOnMorphismsWithGivenLeftInternalHoms</code>( <var class="Arg">s</var>, <var class="Arg">alpha</var>, <var class="Arg">beta</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( s, r )</span></p>

<p>The arguments are an object <span class="Math">s = \mathrm{\underline{Hom}_\ell}(a',b)</span>, two morphisms <span class="Math">\alpha: a \rightarrow a', \beta: b \rightarrow b'</span>, and an object <span class="Math">r = \mathrm{\underline{Hom}_\ell}(a,b')</span>. The output is the internal hom morphism <span class="Math">\mathrm{\underline{Hom}_\ell}(\alpha,\beta): \mathrm{\underline{Hom}_\ell}(a',b) \rightarrow \mathrm{\underline{Hom}_\ell}(a,b')</span>.</p>

<p><a id="X82C4FACF83C3611D" name="X82C4FACF83C3611D"></a></p>

<h5>1.5-4 LeftClosedMonoidalEvaluationMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftClosedMonoidalEvaluationMorphism</code>( <var class="Arg">a</var>, <var class="Arg">b</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( \mathrm{\underline{Hom}_\ell}(a,b) \otimes a, b )</span>.</p>

<p>The arguments are two objects <span class="Math">a, b</span>. The output is the evaluation morphism <span class="Math">\mathrm{ev}_{a,b}: \mathrm{\underline{Hom}_\ell}(a,b) \otimes a \rightarrow b</span>, i.e., the counit of the tensor hom adjunction.</p>

<p><a id="X8575A3748713EACF" name="X8575A3748713EACF"></a></p>

<h5>1.5-5 LeftClosedMonoidalEvaluationMorphismWithGivenSource</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftClosedMonoidalEvaluationMorphismWithGivenSource</code>( <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">s</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( s, b )</span>.</p>

<p>The arguments are two objects <span class="Math">a,b</span> and an object <span class="Math">s = \mathrm{\underline{Hom}_\ell}(a,b) \otimes a</span>. The output is the evaluation morphism <span class="Math">\mathrm{ev}_{a,b}: \mathrm{\underline{Hom}_\ell}(a,b) \otimes a \rightarrow b</span>, i.e., the counit of the tensor hom adjunction.</p>

<p><a id="X7A526C59812F2A59" name="X7A526C59812F2A59"></a></p>

<h5>1.5-6 LeftClosedMonoidalCoevaluationMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftClosedMonoidalCoevaluationMorphism</code>( <var class="Arg">a</var>, <var class="Arg">b</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( b, \mathrm{\underline{Hom}_\ell}(a, b \otimes a) )</span>.</p>

<p>The arguments are two objects <span class="Math">a,b</span>. The output is the coevaluation morphism <span class="Math">\mathrm{coev}_{a,b}: b \rightarrow \mathrm{\underline{Hom}_\ell}(a, b \otimes a)</span>, i.e., the unit of the tensor hom adjunction.</p>

<p><a id="X7BC7F1497A00E87A" name="X7BC7F1497A00E87A"></a></p>

<h5>1.5-7 LeftClosedMonoidalCoevaluationMorphismWithGivenRange</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftClosedMonoidalCoevaluationMorphismWithGivenRange</code>( <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( b, r )</span>.</p>

<p>The arguments are two objects <span class="Math">a,b</span> and an object <span class="Math">r = \mathrm{\underline{Hom}_\ell}(a, b \otimes a)</span>. The output is the coevaluation morphism <span class="Math">\mathrm{coev}_{a,b}: b \rightarrow \mathrm{\underline{Hom}_\ell}(a, b \otimes a)</span>, i.e., the unit of the tensor hom adjunction.</p>

<p><a id="X83A5A47979C9B92D" name="X83A5A47979C9B92D"></a></p>

<h5>1.5-8 TensorProductToLeftInternalHomAdjunctMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TensorProductToLeftInternalHomAdjunctMorphism</code>( <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">f</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( a, \mathrm{\underline{Hom}_\ell}(b,c) )</span>.</p>

<p>The arguments are two objects <span class="Math">a,b</span> and a morphism <span class="Math">f: a \otimes b \rightarrow c</span>. The output is a morphism <span class="Math">g: a \rightarrow \mathrm{\underline{Hom}_\ell}(b,c)</span> corresponding to <span class="Math">f</span> under the tensor hom adjunction.</p>

<p><a id="X7BB734AA7F213B47" name="X7BB734AA7F213B47"></a></p>

<h5>1.5-9 TensorProductToLeftInternalHomAdjunctMorphismWithGivenLeftInternalHom</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TensorProductToLeftInternalHomAdjunctMorphismWithGivenLeftInternalHom</code>( <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">f</var>, <var class="Arg">i</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( a, i )</span>.</p>

<p>The arguments are two objects <span class="Math">a,b</span>, a morphism <span class="Math">f: a \otimes b \rightarrow c</span> and an object <span class="Math">i = \mathrm{\underline{Hom}_\ell}(b,c)</span>. The output is a morphism <span class="Math">g: a \rightarrow \mathrm{\underline{Hom}_\ell}(b,c)</span> corresponding to <span class="Math">f</span> under the tensor hom adjunction.</p>

<p><a id="X7C7D769879A7DA90" name="X7C7D769879A7DA90"></a></p>

<h5>1.5-10 LeftInternalHomToTensorProductAdjunctMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftInternalHomToTensorProductAdjunctMorphism</code>( <var class="Arg">b</var>, <var class="Arg">c</var>, <var class="Arg">g</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(a \otimes b, c)</span>.</p>

<p>The arguments are two objects <span class="Math">b,c</span> and a morphism <span class="Math">g: a \rightarrow \mathrm{\underline{Hom}_\ell}(b,c)</span>. The output is a morphism <span class="Math">f: a \otimes b \rightarrow c</span> corresponding to <span class="Math">g</span> under the tensor hom adjunction.</p>

<p><a id="X80431C73861AEC43" name="X80431C73861AEC43"></a></p>

<h5>1.5-11 LeftInternalHomToTensorProductAdjunctMorphismWithGivenTensorProduct</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftInternalHomToTensorProductAdjunctMorphismWithGivenTensorProduct</code>( <var class="Arg">b</var>, <var class="Arg">c</var>, <var class="Arg">g</var>, <var class="Arg">t</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(t, c)</span>.</p>

<p>The arguments are two objects <span class="Math">b,c</span>, a morphism <span class="Math">g: a \rightarrow \mathrm{\underline{Hom}_\ell}(b,c)</span> and an object <span class="Math">t = a \otimes b</span>. The output is a morphism <span class="Math">f: a \otimes b \rightarrow c</span> corresponding to <span class="Math">g</span> under the tensor hom adjunction.</p>

<p><a id="X79AC308B847F5177" name="X79AC308B847F5177"></a></p>

<h5>1.5-12 LeftClosedMonoidalPreComposeMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftClosedMonoidalPreComposeMorphism</code>( <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">c</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( \mathrm{\underline{Hom}_\ell}(a,b) \otimes \mathrm{\underline{Hom}_\ell}(b,c), \mathrm{\underline{Hom}_\ell}(a,c) )</span>.</p>

<p>The arguments are three objects <span class="Math">a,b,c</span>. The output is the precomposition morphism <span class="Math">\mathrm{LeftClosedMonoidalPreComposeMorphism}_{a,b,c}: \mathrm{\underline{Hom}_\ell}(a,b) \otimes \mathrm{\underline{Hom}_\ell}(b,c) \rightarrow \mathrm{\underline{Hom}_\ell}(a,c)</span>.</p>

<p><a id="X78E3E67480AC81F4" name="X78E3E67480AC81F4"></a></p>

<h5>1.5-13 LeftClosedMonoidalPreComposeMorphismWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftClosedMonoidalPreComposeMorphismWithGivenObjects</code>( <var class="Arg">s</var>, <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">c</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( s, r )</span>.</p>

<p>The arguments are an object <span class="Math">s = \mathrm{\underline{Hom}_\ell}(a,b) \otimes \mathrm{\underline{Hom}_\ell}(b,c)</span>, three objects <span class="Math">a,b,c</span>, and an object <span class="Math">r = \mathrm{\underline{Hom}_\ell}(a,c)</span>. The output is the precomposition morphism <span class="Math">\mathrm{LeftClosedMonoidalPreComposeMorphismWithGivenObjects}_{a,b,c}: \mathrm{\underline{Hom}_\ell}(a,b) \otimes \mathrm{\underline{Hom}_\ell}(b,c) \rightarrow \mathrm{\underline{Hom}_\ell}(a,c)</span>.</p>

<p><a id="X7CFBE32D7F8F16CD" name="X7CFBE32D7F8F16CD"></a></p>

<h5>1.5-14 LeftClosedMonoidalPostComposeMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftClosedMonoidalPostComposeMorphism</code>( <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">c</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( \mathrm{\underline{Hom}_\ell}(b,c) \otimes \mathrm{\underline{Hom}_\ell}(a,b), \mathrm{\underline{Hom}_\ell}(a,c) )</span>.</p>

<p>The arguments are three objects <span class="Math">a,b,c</span>. The output is the postcomposition morphism <span class="Math">\mathrm{LeftClosedMonoidalPostComposeMorphism}_{a,b,c}: \mathrm{\underline{Hom}_\ell}(b,c) \otimes \mathrm{\underline{Hom}_\ell}(a,b) \rightarrow \mathrm{\underline{Hom}_\ell}(a,c)</span>.</p>

<p><a id="X7D5E05257D908A56" name="X7D5E05257D908A56"></a></p>

<h5>1.5-15 LeftClosedMonoidalPostComposeMorphismWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftClosedMonoidalPostComposeMorphismWithGivenObjects</code>( <var class="Arg">s</var>, <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">c</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( s, r )</span>.</p>

<p>The arguments are an object <span class="Math">s = \mathrm{\underline{Hom}_\ell}(b,c) \otimes \mathrm{\underline{Hom}_\ell}(a,b)</span>, three objects <span class="Math">a,b,c</span>, and an object <span class="Math">r = \mathrm{\underline{Hom}_\ell}(a,c)</span>. The output is the postcomposition morphism <span class="Math">\mathrm{LeftClosedMonoidalPostComposeMorphismWithGivenObjects}_{a,b,c}: \mathrm{\underline{Hom}_\ell}(b,c) \otimes \mathrm{\underline{Hom}_\ell}(a,b) \rightarrow \mathrm{\underline{Hom}_\ell}(a,c)</span>.</p>

<p><a id="X859959ED7F2CFDCC" name="X859959ED7F2CFDCC"></a></p>

<h5>1.5-16 LeftDualOnObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftDualOnObjects</code>( <var class="Arg">a</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: an object</p>

<p>The argument is an object <span class="Math">a</span>. The output is its dual object <span class="Math">a^{\vee}</span>.</p>

<p><a id="X7B697FFC7B23A48B" name="X7B697FFC7B23A48B"></a></p>

<h5>1.5-17 LeftDualOnMorphisms</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftDualOnMorphisms</code>( <var class="Arg">alpha</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( b^{\vee}, a^{\vee} )</span>.</p>

<p>The argument is a morphism <span class="Math">\alpha: a \rightarrow b</span>. The output is its dual morphism <span class="Math">\alpha^{\vee}: b^{\vee} \rightarrow a^{\vee}</span>.</p>

<p><a id="X8282E454874316D8" name="X8282E454874316D8"></a></p>

<h5>1.5-18 LeftDualOnMorphismsWithGivenLeftDuals</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftDualOnMorphismsWithGivenLeftDuals</code>( <var class="Arg">s</var>, <var class="Arg">alpha</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( s, r )</span>.</p>

<p>The argument is an object <span class="Math">s = b^{\vee}</span>, a morphism <span class="Math">\alpha: a \rightarrow b</span>, and an object <span class="Math">r = a^{\vee}</span>. The output is the dual morphism <span class="Math">\alpha^{\vee}: b^{\vee} \rightarrow a^{\vee}</span>.</p>

<p><a id="X7FF3227087ABDA8E" name="X7FF3227087ABDA8E"></a></p>

<h5>1.5-19 LeftClosedMonoidalEvaluationForLeftDual</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftClosedMonoidalEvaluationForLeftDual</code>( <var class="Arg">a</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( a^{\vee} \otimes a, 1 )</span>.</p>

<p>The argument is an object <span class="Math">a</span>. The output is the evaluation morphism <span class="Math">\mathrm{ev}_{a}: a^{\vee} \otimes a \rightarrow 1</span>.</p>

<p><a id="X86995E4D7A63E68F" name="X86995E4D7A63E68F"></a></p>

<h5>1.5-20 LeftClosedMonoidalEvaluationForLeftDualWithGivenTensorProduct</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftClosedMonoidalEvaluationForLeftDualWithGivenTensorProduct</code>( <var class="Arg">s</var>, <var class="Arg">a</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( s, r )</span>.</p>

<p>The arguments are an object <span class="Math">s = a^{\vee} \otimes a</span>, an object <span class="Math">a</span>, and an object <span class="Math">r = 1</span>. The output is the evaluation morphism <span class="Math">\mathrm{ev}_{a}: a^{\vee} \otimes a \rightarrow 1</span>.</p>

<p><a id="X85D2B94A85E3DBD5" name="X85D2B94A85E3DBD5"></a></p>

<h5>1.5-21 MorphismToLeftBidual</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ MorphismToLeftBidual</code>( <var class="Arg">a</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(a, (a^{\vee})^{\vee})</span>.</p>

<p>The argument is an object <span class="Math">a</span>. The output is the morphism to the bidual <span class="Math">a \rightarrow (a^{\vee})^{\vee}</span>.</p>

<p><a id="X868774B68189D7E9" name="X868774B68189D7E9"></a></p>

<h5>1.5-22 MorphismToLeftBidualWithGivenLeftBidual</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ MorphismToLeftBidualWithGivenLeftBidual</code>( <var class="Arg">a</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(a, r)</span>.</p>

<p>The arguments are an object <span class="Math">a</span>, and an object <span class="Math">r = (a^{\vee})^{\vee}</span>. The output is the morphism to the bidual <span class="Math">a \rightarrow (a^{\vee})^{\vee}</span>.</p>

<p><a id="X7939CEE8854017D2" name="X7939CEE8854017D2"></a></p>

<h5>1.5-23 TensorProductLeftInternalHomCompatibilityMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TensorProductLeftInternalHomCompatibilityMorphism</code>( <var class="Arg">list</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( \mathrm{\underline{Hom}_\ell}(a,a') \otimes \mathrm{\underline{Hom}_\ell}(b,b'), \mathrm{\underline{Hom}_\ell}(a \otimes b,a' \otimes b'))</span>.</p>

<p>The argument is a list of four objects <span class="Math">[ a, a', b, b' ]</span>. The output is the natural morphism <span class="Math">\mathrm{TensorProductLeftInternalHomCompatibilityMorphism}_{a,a',b,b'}: \mathrm{\underline{Hom}_\ell}(a,a') \otimes \mathrm{\underline{Hom}_\ell}(b,b') \rightarrow \mathrm{\underline{Hom}_\ell}(a \otimes b,a' \otimes b')</span>.</p>

<p><a id="X798C160A84CA5623" name="X798C160A84CA5623"></a></p>

<h5>1.5-24 TensorProductLeftInternalHomCompatibilityMorphismWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TensorProductLeftInternalHomCompatibilityMorphismWithGivenObjects</code>( <var class="Arg">s</var>, <var class="Arg">list</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( s, r )</span>.</p>

<p>The arguments are a list of four objects <span class="Math">[ a, a', b, b' ]</span>, and two objects <span class="Math">s = \mathrm{\underline{Hom}_\ell}(a,a') \otimes \mathrm{\underline{Hom}_\ell}(b,b')</span> and <span class="Math">r = \mathrm{\underline{Hom}_\ell}(a \otimes b,a' \otimes b')</span>. The output is the natural morphism <span class="Math">\mathrm{TensorProductLeftInternalHomCompatibilityMorphismWithGivenObjects}_{a,a',b,b'}: \mathrm{\underline{Hom}_\ell}(a,a') \otimes \mathrm{\underline{Hom}_\ell}(b,b') \rightarrow \mathrm{\underline{Hom}_\ell}(a \otimes b,a' \otimes b')</span>.</p>

<p><a id="X8635D47E7835C8AA" name="X8635D47E7835C8AA"></a></p>

<h5>1.5-25 TensorProductLeftDualityCompatibilityMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TensorProductLeftDualityCompatibilityMorphism</code>( <var class="Arg">a</var>, <var class="Arg">b</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( a^{\vee} \otimes b^{\vee}, (a \otimes b)^{\vee} )</span>.</p>

<p>The arguments are two objects <span class="Math">a,b</span>. The output is the natural morphism <span class="Math">\mathrm{TensorProductLeftDualityCompatibilityMorphism}: a^{\vee} \otimes b^{\vee} \rightarrow (a \otimes b)^{\vee}</span>.</p>

<p><a id="X8435799E83221130" name="X8435799E83221130"></a></p>

<h5>1.5-26 TensorProductLeftDualityCompatibilityMorphismWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TensorProductLeftDualityCompatibilityMorphismWithGivenObjects</code>( <var class="Arg">s</var>, <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( s, r )</span>.</p>

<p>The arguments are an object <span class="Math">s = a^{\vee} \otimes b^{\vee}</span>, two objects <span class="Math">a,b</span>, and an object <span class="Math">r = (a \otimes b)^{\vee}</span>. The output is the natural morphism <span class="Math">\mathrm{TensorProductLeftDualityCompatibilityMorphismWithGivenObjects}_{a,b}: a^{\vee} \otimes b^{\vee} \rightarrow (a \otimes b)^{\vee}</span>.</p>

<p><a id="X80FE157E81B02827" name="X80FE157E81B02827"></a></p>

<h5>1.5-27 MorphismFromTensorProductToLeftInternalHom</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ MorphismFromTensorProductToLeftInternalHom</code>( <var class="Arg">a</var>, <var class="Arg">b</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( a^{\vee} \otimes b, \mathrm{\underline{Hom}_\ell}(a,b) )</span>.</p>

<p>The arguments are two objects <span class="Math">a,b</span>. The output is the natural morphism <span class="Math">\mathrm{MorphismFromTensorProductToLeftInternalHom}_{a,b}: a^{\vee} \otimes b \rightarrow \mathrm{\underline{Hom}_\ell}(a,b)</span>.</p>

<p><a id="X78FDDC2986E50825" name="X78FDDC2986E50825"></a></p>

<h5>1.5-28 MorphismFromTensorProductToLeftInternalHomWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ MorphismFromTensorProductToLeftInternalHomWithGivenObjects</code>( <var class="Arg">s</var>, <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( s, r )</span>.</p>

<p>The arguments are an object <span class="Math">s = a^{\vee} \otimes b</span>, two objects <span class="Math">a,b</span>, and an object <span class="Math">r = \mathrm{\underline{Hom}_\ell}(a,b)</span>. The output is the natural morphism <span class="Math">\mathrm{MorphismFromTensorProductToLeftInternalHomWithGivenObjects}_{a,b}: a^{\vee} \otimes b \rightarrow \mathrm{\underline{Hom}_\ell}(a,b)</span>.</p>

<p><a id="X7EA425DA848670D9" name="X7EA425DA848670D9"></a></p>

<h5>1.5-29 IsomorphismFromLeftDualObjectToLeftInternalHomIntoTensorUnit</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsomorphismFromLeftDualObjectToLeftInternalHomIntoTensorUnit</code>( <var class="Arg">a</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(a^{\vee}, \mathrm{\underline{Hom}_\ell}(a,1))</span>.</p>

<p>The argument is an object <span class="Math">a</span>. The output is the isomorphism <span class="Math">\mathrm{IsomorphismFromLeftDualObjectToLeftInternalHomIntoTensorUnit}_{a}: a^{\vee} \rightarrow \mathrm{\underline{Hom}_\ell}(a,1)</span>.</p>

<p><a id="X781A2D417A8BC8DF" name="X781A2D417A8BC8DF"></a></p>

<h5>1.5-30 IsomorphismFromLeftInternalHomIntoTensorUnitToLeftDualObject</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsomorphismFromLeftInternalHomIntoTensorUnitToLeftDualObject</code>( <var class="Arg">a</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(\mathrm{\underline{Hom}_\ell}(a,1), a^{\vee})</span>.</p>

<p>The argument is an object <span class="Math">a</span>. The output is the isomorphism <span class="Math">\mathrm{IsomorphismFromLeftInternalHomIntoTensorUnitToLeftDualObject}_{a}: \mathrm{\underline{Hom}_\ell}(a,1) \rightarrow a^{\vee}</span>.</p>

<p><a id="X82D9D78C7A8DA61A" name="X82D9D78C7A8DA61A"></a></p>

<h5>1.5-31 UniversalPropertyOfLeftDual</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ UniversalPropertyOfLeftDual</code>( <var class="Arg">t</var>, <var class="Arg">a</var>, <var class="Arg">alpha</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(t, a^{\vee})</span>.</p>

<p>The arguments are two objects <span class="Math">t,a</span>, and a morphism <span class="Math">\alpha: t \otimes a \rightarrow 1</span>. The output is the morphism <span class="Math">t \rightarrow a^{\vee}</span> given by the universal property of <span class="Math">a^{\vee}</span>.</p>

<p><a id="X7C7A252A78484873" name="X7C7A252A78484873"></a></p>

<h5>1.5-32 LeftClosedMonoidalLambdaIntroduction</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftClosedMonoidalLambdaIntroduction</code>( <var class="Arg">alpha</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( 1, \mathrm{\underline{Hom}_\ell}(a,b) )</span>.</p>

<p>The argument is a morphism <span class="Math">\alpha: a \rightarrow b</span>. The output is the corresponding morphism <span class="Math">1 \rightarrow \mathrm{\underline{Hom}_\ell}(a,b)</span> under the tensor hom adjunction.</p>

<p><a id="X83B3A8FA8363F620" name="X83B3A8FA8363F620"></a></p>

<h5>1.5-33 LeftClosedMonoidalLambdaElimination</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftClosedMonoidalLambdaElimination</code>( <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">alpha</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(a,b)</span>.</p>

<p>The arguments are two objects <span class="Math">a,b</span>, and a morphism <span class="Math">\alpha: 1 \rightarrow \mathrm{\underline{Hom}_\ell}(a,b)</span>. The output is a morphism <span class="Math">a \rightarrow b</span> corresponding to <span class="Math">\alpha</span> under the tensor hom adjunction.</p>

<p><a id="X7ECAB43778388C41" name="X7ECAB43778388C41"></a></p>

<h5>1.5-34 IsomorphismFromObjectToLeftInternalHom</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsomorphismFromObjectToLeftInternalHom</code>( <var class="Arg">a</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(a, \mathrm{\underline{Hom}_\ell}(1,a))</span>.</p>

<p>The argument is an object <span class="Math">a</span>. The output is the natural isomorphism <span class="Math">a \rightarrow \mathrm{\underline{Hom}_\ell}(1,a)</span>.</p>

<p><a id="X874D7D8E81A6AFF1" name="X874D7D8E81A6AFF1"></a></p>

<h5>1.5-35 IsomorphismFromObjectToLeftInternalHomWithGivenLeftInternalHom</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsomorphismFromObjectToLeftInternalHomWithGivenLeftInternalHom</code>( <var class="Arg">a</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(a, r)</span>.</p>

<p>The argument is an object <span class="Math">a</span>, and an object <span class="Math">r = \mathrm{\underline{Hom}_\ell}(1,a)</span>. The output is the natural isomorphism <span class="Math">a \rightarrow \mathrm{\underline{Hom}_\ell}(1,a)</span>.</p>

<p><a id="X7908CF267DDAA38C" name="X7908CF267DDAA38C"></a></p>

<h5>1.5-36 IsomorphismFromLeftInternalHomToObject</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsomorphismFromLeftInternalHomToObject</code>( <var class="Arg">a</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(\mathrm{\underline{Hom}_\ell}(1,a),a)</span>.</p>

<p>The argument is an object <span class="Math">a</span>. The output is the natural isomorphism <span class="Math">\mathrm{\underline{Hom}_\ell}(1,a) \rightarrow a</span>.</p>

<p><a id="X7B2F235C8444803C" name="X7B2F235C8444803C"></a></p>

<h5>1.5-37 IsomorphismFromLeftInternalHomToObjectWithGivenLeftInternalHom</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsomorphismFromLeftInternalHomToObjectWithGivenLeftInternalHom</code>( <var class="Arg">a</var>, <var class="Arg">s</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(s,a)</span>.</p>

<p>The argument is an object <span class="Math">a</span>, and an object <span class="Math">s = \mathrm{\underline{Hom}_\ell}(1,a)</span>. The output is the natural isomorphism <span class="Math">\mathrm{\underline{Hom}_\ell}(1,a) \rightarrow a</span>.</p>

<p><a id="X7BC682067A30E580" name="X7BC682067A30E580"></a></p>

<h4>1.6 <span class="Heading">Closed Monoidal Categories</span></h4>

<p>A monoidal category <span class="Math">\mathbf{C}</span> which has for each functor <span class="Math">- \otimes b: \mathbf{C} \rightarrow \mathbf{C}</span> a right adjoint (denoted by <span class="Math">\mathrm{\underline{Hom}_\ell}(b,-)</span>) is called a <em>closed monoidal category</em>.</p>

<p>If no operations involving duals are installed manually, the dual objects will be derived as <span class="Math">a^\vee \coloneqq \mathrm{\underline{Hom}_\ell}(a,1)</span>.</p>

<p>The corresponding GAP property is called <code class="code">IsClosedMonoidalCategory</code>.</p>

<p><a id="X78AA83E77B380D68" name="X78AA83E77B380D68"></a></p>

<h5>1.6-1 InternalHomOnObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ InternalHomOnObjects</code>( <var class="Arg">a</var>, <var class="Arg">b</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: an object</p>

<p>The arguments are two objects <span class="Math">a,b</span>. The output is the internal hom object <span class="Math">\mathrm{\underline{Hom}}(a,b)</span>.</p>

<p><a id="X7C0191A483A72F98" name="X7C0191A483A72F98"></a></p>

<h5>1.6-2 InternalHomOnMorphisms</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ InternalHomOnMorphisms</code>( <var class="Arg">alpha</var>, <var class="Arg">beta</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( \mathrm{\underline{Hom}}(a',b), \mathrm{\underline{Hom}}(a,b') )</span></p>

<p>The arguments are two morphisms <span class="Math">\alpha: a \rightarrow a', \beta: b \rightarrow b'</span>. The output is the internal hom morphism <span class="Math">\mathrm{\underline{Hom}}(\alpha,\beta): \mathrm{\underline{Hom}}(a',b) \rightarrow \mathrm{\underline{Hom}}(a,b')</span>.</p>

<p><a id="X861226B47B5CB713" name="X861226B47B5CB713"></a></p>

<h5>1.6-3 InternalHomOnMorphismsWithGivenInternalHoms</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ InternalHomOnMorphismsWithGivenInternalHoms</code>( <var class="Arg">s</var>, <var class="Arg">alpha</var>, <var class="Arg">beta</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( s, r )</span></p>

<p>The arguments are an object <span class="Math">s = \mathrm{\underline{Hom}}(a',b)</span>, two morphisms <span class="Math">\alpha: a \rightarrow a', \beta: b \rightarrow b'</span>, and an object <span class="Math">r = \mathrm{\underline{Hom}}(a,b')</span>. The output is the internal hom morphism <span class="Math">\mathrm{\underline{Hom}}(\alpha,\beta): \mathrm{\underline{Hom}}(a',b) \rightarrow \mathrm{\underline{Hom}}(a,b')</span>.</p>

<p><a id="X844F05DF7DE23F99" name="X844F05DF7DE23F99"></a></p>

<h5>1.6-4 ClosedMonoidalRightEvaluationMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ClosedMonoidalRightEvaluationMorphism</code>( <var class="Arg">a</var>, <var class="Arg">b</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(a \otimes \mathrm{\underline{Hom}}(a,b), b )</span>.</p>

<p>The arguments are two objects <span class="Math">a, b</span>. The output is the right evaluation morphism <span class="Math">\mathrm{ev}_{a,b}:a \otimes \mathrm{\underline{Hom}}(a,b) \rightarrow b</span>, i.e., the counit of the tensor hom adjunction.</p>

<p><a id="X83E6461280B0EB0C" name="X83E6461280B0EB0C"></a></p>

<h5>1.6-5 ClosedMonoidalRightEvaluationMorphismWithGivenSource</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ClosedMonoidalRightEvaluationMorphismWithGivenSource</code>( <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">s</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( s, b )</span>.</p>

<p>The arguments are two objects <span class="Math">a,b</span> and an object <span class="Math">s = a \otimes \mathrm{\underline{Hom}}(a,b)</span>. The output is the right evaluation morphism <span class="Math">\mathrm{ev}_{a,b}: a \otimes \mathrm{\underline{Hom}}(a,b) \rightarrow b</span>, i.e., the counit of the tensor hom adjunction.</p>

<p><a id="X7A745E5A836B5E91" name="X7A745E5A836B5E91"></a></p>

<h5>1.6-6 ClosedMonoidalRightCoevaluationMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ClosedMonoidalRightCoevaluationMorphism</code>( <var class="Arg">a</var>, <var class="Arg">b</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( b, \mathrm{\underline{Hom}}(a, a \otimes b) )</span>.</p>

<p>The arguments are two objects <span class="Math">a,b</span>. The output is the right coevaluation morphism <span class="Math">\mathrm{coev}_{a,b}: b \rightarrow \mathrm{\underline{Hom}}(a, a \otimes b)</span>, i.e., the unit of the tensor hom adjunction.</p>

<p><a id="X868AD1A278EBAB03" name="X868AD1A278EBAB03"></a></p>

<h5>1.6-7 ClosedMonoidalRightCoevaluationMorphismWithGivenRange</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ClosedMonoidalRightCoevaluationMorphismWithGivenRange</code>( <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( b, r )</span>.</p>

<p>The arguments are two objects <span class="Math">a,b</span> and an object <span class="Math">r = \mathrm{\underline{Hom}}(a, a \otimes b)</span>. The output is the right coevaluation morphism <span class="Math">\mathrm{coev}_{a,b}: b \rightarrow \mathrm{\underline{Hom}}(a, a \otimes b)</span>, i.e., the unit of the tensor hom adjunction.</p>

<p><a id="X7BA9C4A184346304" name="X7BA9C4A184346304"></a></p>

<h5>1.6-8 TensorProductToInternalHomRightAdjunctMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TensorProductToInternalHomRightAdjunctMorphism</code>( <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">f</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( b, \mathrm{\underline{Hom}}(a,c) )</span>.</p>

<p>The arguments are two objects <span class="Math">a,b</span> and a morphism <span class="Math">f: a \otimes b \rightarrow c</span>. The output is a morphism <span class="Math">g: b \rightarrow \mathrm{\underline{Hom}}(a,c)</span> corresponding to <span class="Math">f</span> under the tensor hom adjunction.</p>

<p><a id="X8218B01287CD44E5" name="X8218B01287CD44E5"></a></p>

<h5>1.6-9 TensorProductToInternalHomRightAdjunctMorphismWithGivenInternalHom</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TensorProductToInternalHomRightAdjunctMorphismWithGivenInternalHom</code>( <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">f</var>, <var class="Arg">i</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( b, i )</span>.</p>

<p>The arguments are two objects <span class="Math">a,b</span>, a morphism <span class="Math">f: a \otimes b \rightarrow c</span> and an object <span class="Math">i = \mathrm{\underline{Hom}}(a,c)</span>. The output is a morphism <span class="Math">g: b \rightarrow i</span> corresponding to <span class="Math">f</span> under the tensor hom adjunction.</p>

<p><a id="X78A16762823E5F1C" name="X78A16762823E5F1C"></a></p>

<h5>1.6-10 TensorProductToInternalHomRightAdjunctionIsomorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TensorProductToInternalHomRightAdjunctionIsomorphism</code>( <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">c</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( H(a \otimes b, c), H(b, \mathrm{\underline{Hom}}(a,c)) )</span>.</p>

<p>The arguments are three objects <span class="Math">a,b,c</span>. The output is the tri-natural isomorphism <span class="Math">H(a \otimes b, c) \to H(b, \mathrm{\underline{Hom}}(a,c))</span> in the range category of the homomorphism structure <span class="Math">H</span>.</p>

<p><a id="X81D37FA282FC8F11" name="X81D37FA282FC8F11"></a></p>

<h5>1.6-11 TensorProductToInternalHomRightAdjunctionIsomorphismWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TensorProductToInternalHomRightAdjunctionIsomorphismWithGivenObjects</code>( <var class="Arg">s</var>, <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">c</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( s, r )</span>.</p>

<p>The arguments are fives objects <span class="Math">s,a,b,c,r</span> where <span class="Math">s = H(a \otimes b, c)</span> and <span class="Math">r = H(b, \mathrm{\underline{Hom}}(a,c))</span>. The output is the tri-natural isomorphism <span class="Math">s \to r</span> in the range category of the homomorphism structure <span class="Math">H</span>.</p>

<p><a id="X8271B2767A2DFE76" name="X8271B2767A2DFE76"></a></p>

<h5>1.6-12 InternalHomToTensorProductRightAdjunctMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ InternalHomToTensorProductRightAdjunctMorphism</code>( <var class="Arg">a</var>, <var class="Arg">c</var>, <var class="Arg">g</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(a \otimes b, c)</span>.</p>

<p>The arguments are two objects <span class="Math">a,c</span> and a morphism <span class="Math">g: b \rightarrow \mathrm{\underline{Hom}}(a,c)</span>. The output is a morphism <span class="Math">f: a \otimes b \rightarrow c</span> corresponding to <span class="Math">g</span> under the tensor hom adjunction.</p>

<p><a id="X7ACBB0CE7FA4C781" name="X7ACBB0CE7FA4C781"></a></p>

<h5>1.6-13 InternalHomToTensorProductRightAdjunctMorphismWithGivenTensorProduct</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ InternalHomToTensorProductRightAdjunctMorphismWithGivenTensorProduct</code>( <var class="Arg">a</var>, <var class="Arg">c</var>, <var class="Arg">g</var>, <var class="Arg">s</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(s, c)</span>.</p>

<p>The arguments are two objects <span class="Math">a,c</span>, a morphism <span class="Math">g: b \rightarrow \mathrm{\underline{Hom}}(a,c)</span> and an object <span class="Math">s = a \otimes b</span>. The output is a morphism <span class="Math">f: s \rightarrow c</span> corresponding to <span class="Math">g</span> under the tensor hom adjunction.</p>

<p><a id="X79EEE4757C27C26E" name="X79EEE4757C27C26E"></a></p>

<h5>1.6-14 InternalHomToTensorProductRightAdjunctionIsomorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ InternalHomToTensorProductRightAdjunctionIsomorphism</code>( <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">c</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( H(b, \mathrm{\underline{Hom}}(a,c)), H(a \otimes b, c) )</span>.</p>

<p>The arguments are three objects <span class="Math">a,b,c</span>. The output is the tri-natural isomorphism <span class="Math">H(b, \mathrm{\underline{Hom}}(a,c)) \to H(a \otimes b, c)</span> in the range category of the homomorphism structure <span class="Math">H</span>.</p>

<p><a id="X7B4CD74A7CE51263" name="X7B4CD74A7CE51263"></a></p>

<h5>1.6-15 InternalHomToTensorProductRightAdjunctionIsomorphismWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ InternalHomToTensorProductRightAdjunctionIsomorphismWithGivenObjects</code>( <var class="Arg">s</var>, <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">c</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( s, r )</span>.</p>

<p>The arguments are fives objects <span class="Math">s,a,b,c,r</span> where <span class="Math">s = H(b, \mathrm{\underline{Hom}}(a,c))</span> and <span class="Math">r = H(a \otimes b, c)</span>. The output is the tri-natural isomorphism <span class="Math">s \to r</span> in the range category of the homomorphism structure <span class="Math">H</span>.</p>

<p><a id="X80B3C53A854B515B" name="X80B3C53A854B515B"></a></p>

<h5>1.6-16 ClosedMonoidalLeftEvaluationMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ClosedMonoidalLeftEvaluationMorphism</code>( <var class="Arg">a</var>, <var class="Arg">b</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( \mathrm{\underline{Hom}}(a,b) \otimes a, b )</span>.</p>

<p>The arguments are two objects <span class="Math">a, b</span>. The output is the left evaluation morphism <span class="Math">\mathrm{ev}_{a,b}: \mathrm{\underline{Hom}}(a,b) \otimes a \rightarrow b</span>, i.e., the counit of the tensor hom adjunction.</p>

<p><a id="X84E1E136819BDA89" name="X84E1E136819BDA89"></a></p>

<h5>1.6-17 ClosedMonoidalLeftEvaluationMorphismWithGivenSource</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ClosedMonoidalLeftEvaluationMorphismWithGivenSource</code>( <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">s</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( s, b )</span>.</p>

<p>The arguments are two objects <span class="Math">a,b</span> and an object <span class="Math">s = \mathrm{\underline{Hom}}(a,b) \otimes a</span>. The output is the left evaluation morphism <span class="Math">\mathrm{ev}_{a,b}: \mathrm{\underline{Hom}}(a,b) \otimes a \rightarrow b</span>, i.e., the counit of the tensor hom adjunction.</p>

<p><a id="X7E35DEB787A71A1F" name="X7E35DEB787A71A1F"></a></p>

<h5>1.6-18 ClosedMonoidalLeftCoevaluationMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ClosedMonoidalLeftCoevaluationMorphism</code>( <var class="Arg">a</var>, <var class="Arg">b</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( b, \mathrm{\underline{Hom}}(a, b \otimes a) )</span>.</p>

<p>The arguments are two objects <span class="Math">a,b</span>. The output is the left coevaluation morphism <span class="Math">\mathrm{coev}_{a,b}: b \rightarrow \mathrm{\underline{Hom}}(a, b \otimes a)</span>, i.e., the unit of the tensor hom adjunction.</p>

<p><a id="X8196CE5D7C88D83C" name="X8196CE5D7C88D83C"></a></p>

<h5>1.6-19 ClosedMonoidalLeftCoevaluationMorphismWithGivenRange</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ClosedMonoidalLeftCoevaluationMorphismWithGivenRange</code>( <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( b, r )</span>.</p>

<p>The arguments are two objects <span class="Math">a,b</span> and an object <span class="Math">r = \mathrm{\underline{Hom}}(a, b \otimes a)</span>. The output is the left coevaluation morphism <span class="Math">\mathrm{coev}_{a,b}: b \rightarrow \mathrm{\underline{Hom}}(a, b \otimes a)</span>, i.e., the unit of the tensor hom adjunction.</p>

<p><a id="X80A58B1F80A186BD" name="X80A58B1F80A186BD"></a></p>

<h5>1.6-20 TensorProductToInternalHomLeftAdjunctMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TensorProductToInternalHomLeftAdjunctMorphism</code>( <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">f</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( a, \mathrm{\underline{Hom}}(b,c) )</span>.</p>

<p>The arguments are two objects <span class="Math">a,b</span> and a morphism <span class="Math">f: a \otimes b \rightarrow c</span>. The output is a morphism <span class="Math">g: a \rightarrow \mathrm{\underline{Hom}}(b,c)</span> corresponding to <span class="Math">f</span> under the tensor hom adjunction.</p>

<p><a id="X7CCE373482D60A57" name="X7CCE373482D60A57"></a></p>

<h5>1.6-21 TensorProductToInternalHomLeftAdjunctMorphismWithGivenInternalHom</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TensorProductToInternalHomLeftAdjunctMorphismWithGivenInternalHom</code>( <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">f</var>, <var class="Arg">i</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( a, i )</span>.</p>

<p>The arguments are two objects <span class="Math">a,b</span>, a morphism <span class="Math">f: a \otimes b \rightarrow c</span> and an object <span class="Math">i = \mathrm{\underline{Hom}}(b,c)</span>. The output is a morphism <span class="Math">g: a \rightarrow i</span> corresponding to <span class="Math">f</span> under the tensor hom adjunction.</p>

<p><a id="X793BAA50819573E4" name="X793BAA50819573E4"></a></p>

<h5>1.6-22 TensorProductToInternalHomLeftAdjunctionIsomorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TensorProductToInternalHomLeftAdjunctionIsomorphism</code>( <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">c</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( H(a \otimes b, c), H(a, \mathrm{\underline{Hom}}(b,c)) )</span>.</p>

<p>The arguments are three objects <span class="Math">a,b,c</span>. The output is the tri-natural isomorphism <span class="Math">H(a \otimes b, c) \to H(a, \mathrm{\underline{Hom}}(b,c))</span> in the range category of the homomorphism structure <span class="Math">H</span>.</p>

<p><a id="X791276987824CDF8" name="X791276987824CDF8"></a></p>

<h5>1.6-23 TensorProductToInternalHomLeftAdjunctionIsomorphismWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TensorProductToInternalHomLeftAdjunctionIsomorphismWithGivenObjects</code>( <var class="Arg">s</var>, <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">c</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( s, r )</span>.</p>

<p>The arguments are fives objects <span class="Math">s,a,b,c,r</span> where <span class="Math">s = H(a \otimes b, c)</span> and <span class="Math">r = H(a, \mathrm{\underline{Hom}}(b,c))</span>. The output is the tri-natural isomorphism <span class="Math">s \to r</span> in the range category of the homomorphism structure <span class="Math">H</span>.</p>

<p><a id="X85F426677EB81BCF" name="X85F426677EB81BCF"></a></p>

<h5>1.6-24 InternalHomToTensorProductLeftAdjunctMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ InternalHomToTensorProductLeftAdjunctMorphism</code>( <var class="Arg">b</var>, <var class="Arg">c</var>, <var class="Arg">g</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(a \otimes b, c)</span>.</p>

<p>The arguments are two objects <span class="Math">b,c</span> and a morphism <span class="Math">g: a \rightarrow \mathrm{\underline{Hom}}(b,c)</span>. The output is a morphism <span class="Math">f: a \otimes b \rightarrow c</span> corresponding to <span class="Math">g</span> under the tensor hom adjunction.</p>

<p><a id="X859B738881052D1C" name="X859B738881052D1C"></a></p>

<h5>1.6-25 InternalHomToTensorProductLeftAdjunctMorphismWithGivenTensorProduct</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ InternalHomToTensorProductLeftAdjunctMorphismWithGivenTensorProduct</code>( <var class="Arg">b</var>, <var class="Arg">c</var>, <var class="Arg">g</var>, <var class="Arg">s</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(s, c)</span>.</p>

<p>The arguments are two objects <span class="Math">b,c</span>, a morphism <span class="Math">g: a \rightarrow \mathrm{\underline{Hom}}(b,c)</span> and an object <span class="Math">s = a \otimes b</span>. The output is a morphism <span class="Math">f: s \rightarrow c</span> corresponding to <span class="Math">g</span> under the tensor hom adjunction.</p>

<p><a id="X86AD79F17F8CEE96" name="X86AD79F17F8CEE96"></a></p>

<h5>1.6-26 InternalHomToTensorProductLeftAdjunctionIsomorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ InternalHomToTensorProductLeftAdjunctionIsomorphism</code>( <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">c</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( H(a, \mathrm{\underline{Hom}}(b,c)), H(a \otimes b, c) )</span>.</p>

<p>The arguments are three objects <span class="Math">a,b,c</span>. The output is the tri-natural isomorphism <span class="Math">H(a, \mathrm{\underline{Hom}}(b,c)) \to H(a \otimes b, c)</span> in the range category of the homomorphism structure <span class="Math">H</span>.</p>

<p><a id="X7D707B26863D508A" name="X7D707B26863D508A"></a></p>

<h5>1.6-27 InternalHomToTensorProductLeftAdjunctionIsomorphismWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ InternalHomToTensorProductLeftAdjunctionIsomorphismWithGivenObjects</code>( <var class="Arg">s</var>, <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">c</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( s, r )</span>.</p>

<p>The arguments are fives objects <span class="Math">s,a,b,c,r</span> where <span class="Math">s = H(a, \mathrm{\underline{Hom}}(b,c))</span> and <span class="Math">r = H(a \otimes b, c)</span>. The output is the tri-natural isomorphism <span class="Math">s \to r</span> in the range category of the homomorphism structure <span class="Math">H</span>.</p>

<p><a id="X86E4E97C82BFB45C" name="X86E4E97C82BFB45C"></a></p>

<h5>1.6-28 MonoidalPreComposeMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ MonoidalPreComposeMorphism</code>( <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">c</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( \mathrm{\underline{Hom}}(a,b) \otimes \mathrm{\underline{Hom}}(b,c), \mathrm{\underline{Hom}}(a,c) )</span>.</p>

<p>The arguments are three objects <span class="Math">a,b,c</span>. The output is the precomposition morphism <span class="Math">\mathrm{MonoidalPreComposeMorphism}_{a,b,c}: \mathrm{\underline{Hom}}(a,b) \otimes \mathrm{\underline{Hom}}(b,c) \rightarrow \mathrm{\underline{Hom}}(a,c)</span>.</p>

<p><a id="X7FE4A52284060F20" name="X7FE4A52284060F20"></a></p>

<h5>1.6-29 MonoidalPreComposeMorphismWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ MonoidalPreComposeMorphismWithGivenObjects</code>( <var class="Arg">s</var>, <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">c</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( s, r )</span>.</p>

<p>The arguments are an object <span class="Math">s = \mathrm{\underline{Hom}}(a,b) \otimes \mathrm{\underline{Hom}}(b,c)</span>, three objects <span class="Math">a,b,c</span>, and an object <span class="Math">r = \mathrm{\underline{Hom}}(a,c)</span>. The output is the precomposition morphism <span class="Math">\mathrm{MonoidalPreComposeMorphismWithGivenObjects}_{a,b,c}: \mathrm{\underline{Hom}}(a,b) \otimes \mathrm{\underline{Hom}}(b,c) \rightarrow \mathrm{\underline{Hom}}(a,c)</span>.</p>

<p><a id="X79F4FCE781385829" name="X79F4FCE781385829"></a></p>

<h5>1.6-30 MonoidalPostComposeMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ MonoidalPostComposeMorphism</code>( <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">c</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( \mathrm{\underline{Hom}}(b,c) \otimes \mathrm{\underline{Hom}}(a,b), \mathrm{\underline{Hom}}(a,c) )</span>.</p>

<p>The arguments are three objects <span class="Math">a,b,c</span>. The output is the postcomposition morphism <span class="Math">\mathrm{MonoidalPostComposeMorphism}_{a,b,c}: \mathrm{\underline{Hom}}(b,c) \otimes \mathrm{\underline{Hom}}(a,b) \rightarrow \mathrm{\underline{Hom}}(a,c)</span>.</p>

<p><a id="X7E6933B8816EE4E3" name="X7E6933B8816EE4E3"></a></p>

<h5>1.6-31 MonoidalPostComposeMorphismWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ MonoidalPostComposeMorphismWithGivenObjects</code>( <var class="Arg">s</var>, <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">c</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( s, r )</span>.</p>

<p>The arguments are an object <span class="Math">s = \mathrm{\underline{Hom}}(b,c) \otimes \mathrm{\underline{Hom}}(a,b)</span>, three objects <span class="Math">a,b,c</span>, and an object <span class="Math">r = \mathrm{\underline{Hom}}(a,c)</span>. The output is the postcomposition morphism <span class="Math">\mathrm{MonoidalPostComposeMorphismWithGivenObjects}_{a,b,c}: \mathrm{\underline{Hom}}(b,c) \otimes \mathrm{\underline{Hom}}(a,b) \rightarrow \mathrm{\underline{Hom}}(a,c)</span>.</p>

<p><a id="X80FFC71D7E57DD53" name="X80FFC71D7E57DD53"></a></p>

<h5>1.6-32 DualOnObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ DualOnObjects</code>( <var class="Arg">a</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: an object</p>

<p>The argument is an object <span class="Math">a</span>. The output is its dual object <span class="Math">a^{\vee}</span>.</p>

<p><a id="X815C0BC47D000819" name="X815C0BC47D000819"></a></p>

<h5>1.6-33 DualOnMorphisms</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ DualOnMorphisms</code>( <var class="Arg">alpha</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( b^{\vee}, a^{\vee} )</span>.</p>

<p>The argument is a morphism <span class="Math">\alpha: a \rightarrow b</span>. The output is its dual morphism <span class="Math">\alpha^{\vee}: b^{\vee} \rightarrow a^{\vee}</span>.</p>

<p><a id="X7DCC0F468386AA46" name="X7DCC0F468386AA46"></a></p>

<h5>1.6-34 DualOnMorphismsWithGivenDuals</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ DualOnMorphismsWithGivenDuals</code>( <var class="Arg">s</var>, <var class="Arg">alpha</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( s, r )</span>.</p>

<p>The argument is an object <span class="Math">s = b^{\vee}</span>, a morphism <span class="Math">\alpha: a \rightarrow b</span>, and an object <span class="Math">r = a^{\vee}</span>. The output is the dual morphism <span class="Math">\alpha^{\vee}: b^{\vee} \rightarrow a^{\vee}</span>.</p>

<p><a id="X86D42C7587F03A68" name="X86D42C7587F03A68"></a></p>

<h5>1.6-35 EvaluationForDual</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ EvaluationForDual</code>( <var class="Arg">a</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( a^{\vee} \otimes a, 1 )</span>.</p>

<p>The argument is an object <span class="Math">a</span>. The output is the evaluation morphism <span class="Math">\mathrm{ev}_{a}: a^{\vee} \otimes a \rightarrow 1</span>.</p>

<p><a id="X7B588B1B8472834E" name="X7B588B1B8472834E"></a></p>

<h5>1.6-36 EvaluationForDualWithGivenTensorProduct</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ EvaluationForDualWithGivenTensorProduct</code>( <var class="Arg">s</var>, <var class="Arg">a</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( s, r )</span>.</p>

<p>The arguments are an object <span class="Math">s = a^{\vee} \otimes a</span>, an object <span class="Math">a</span>, and an object <span class="Math">r = 1</span>. The output is the evaluation morphism <span class="Math">\mathrm{ev}_{a}: a^{\vee} \otimes a \rightarrow 1</span>.</p>

<p><a id="X7F68B55781C1DFB1" name="X7F68B55781C1DFB1"></a></p>

<h5>1.6-37 MorphismToBidual</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ MorphismToBidual</code>( <var class="Arg">a</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(a, (a^{\vee})^{\vee})</span>.</p>

<p>The argument is an object <span class="Math">a</span>. The output is the morphism to the bidual <span class="Math">a \rightarrow (a^{\vee})^{\vee}</span>.</p>

<p><a id="X79260E5680F1E741" name="X79260E5680F1E741"></a></p>

<h5>1.6-38 MorphismToBidualWithGivenBidual</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ MorphismToBidualWithGivenBidual</code>( <var class="Arg">a</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(a, r)</span>.</p>

<p>The arguments are an object <span class="Math">a</span>, and an object <span class="Math">r = (a^{\vee})^{\vee}</span>. The output is the morphism to the bidual <span class="Math">a \rightarrow (a^{\vee})^{\vee}</span>.</p>

<p><a id="X80CDA0CB821E08EE" name="X80CDA0CB821E08EE"></a></p>

<h5>1.6-39 TensorProductInternalHomCompatibilityMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TensorProductInternalHomCompatibilityMorphism</code>( <var class="Arg">list</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( \mathrm{\underline{Hom}}(a,a') \otimes \mathrm{\underline{Hom}}(b,b'), \mathrm{\underline{Hom}}(a \otimes b,a' \otimes b'))</span>.</p>

<p>The argument is a list of four objects <span class="Math">[ a, a', b, b' ]</span>. The output is the natural morphism <span class="Math">\mathrm{TensorProductInternalHomCompatibilityMorphism}_{a,a',b,b'}: \mathrm{\underline{Hom}}(a,a') \otimes \mathrm{\underline{Hom}}(b,b') \rightarrow \mathrm{\underline{Hom}}(a \otimes b,a' \otimes b')</span>.</p>

<p><a id="X7B0194A07AB73486" name="X7B0194A07AB73486"></a></p>

<h5>1.6-40 TensorProductInternalHomCompatibilityMorphismWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TensorProductInternalHomCompatibilityMorphismWithGivenObjects</code>( <var class="Arg">s</var>, <var class="Arg">list</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( s, r )</span>.</p>

<p>The arguments are a list of four objects <span class="Math">[ a, a', b, b' ]</span>, and two objects <span class="Math">s = \mathrm{\underline{Hom}}(a,a') \otimes \mathrm{\underline{Hom}}(b,b')</span> and <span class="Math">r = \mathrm{\underline{Hom}}(a \otimes b,a' \otimes b')</span>. The output is the natural morphism <span class="Math">\mathrm{TensorProductInternalHomCompatibilityMorphismWithGivenObjects}_{a,a',b,b'}: \mathrm{\underline{Hom}}(a,a') \otimes \mathrm{\underline{Hom}}(b,b') \rightarrow \mathrm{\underline{Hom}}(a \otimes b,a' \otimes b')</span>.</p>

<p><a id="X7D173DB08132E40A" name="X7D173DB08132E40A"></a></p>

<h5>1.6-41 TensorProductDualityCompatibilityMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TensorProductDualityCompatibilityMorphism</code>( <var class="Arg">a</var>, <var class="Arg">b</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( a^{\vee} \otimes b^{\vee}, (a \otimes b)^{\vee} )</span>.</p>

<p>The arguments are two objects <span class="Math">a,b</span>. The output is the natural morphism <span class="Math">\mathrm{TensorProductDualityCompatibilityMorphism}: a^{\vee} \otimes b^{\vee} \rightarrow (a \otimes b)^{\vee}</span>.</p>

<p><a id="X794ED97782B8DF76" name="X794ED97782B8DF76"></a></p>

<h5>1.6-42 TensorProductDualityCompatibilityMorphismWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TensorProductDualityCompatibilityMorphismWithGivenObjects</code>( <var class="Arg">s</var>, <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( s, r )</span>.</p>

<p>The arguments are an object <span class="Math">s = a^{\vee} \otimes b^{\vee}</span>, two objects <span class="Math">a,b</span>, and an object <span class="Math">r = (a \otimes b)^{\vee}</span>. The output is the natural morphism <span class="Math">\mathrm{TensorProductDualityCompatibilityMorphismWithGivenObjects}_{a,b}: a^{\vee} \otimes b^{\vee} \rightarrow (a \otimes b)^{\vee}</span>.</p>

<p><a id="X8439BFF57BFE390F" name="X8439BFF57BFE390F"></a></p>

<h5>1.6-43 MorphismFromTensorProductToInternalHom</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ MorphismFromTensorProductToInternalHom</code>( <var class="Arg">a</var>, <var class="Arg">b</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( a^{\vee} \otimes b, \mathrm{\underline{Hom}}(a,b) )</span>.</p>

<p>The arguments are two objects <span class="Math">a,b</span>. The output is the natural morphism <span class="Math">\mathrm{MorphismFromTensorProductToInternalHom}_{a,b}: a^{\vee} \otimes b \rightarrow \mathrm{\underline{Hom}}(a,b)</span>.</p>

<p><a id="X8473D28B7F3A5E20" name="X8473D28B7F3A5E20"></a></p>

<h5>1.6-44 MorphismFromTensorProductToInternalHomWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ MorphismFromTensorProductToInternalHomWithGivenObjects</code>( <var class="Arg">s</var>, <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( s, r )</span>.</p>

<p>The arguments are an object <span class="Math">s = a^{\vee} \otimes b</span>, two objects <span class="Math">a,b</span>, and an object <span class="Math">r = \mathrm{\underline{Hom}}(a,b)</span>. The output is the natural morphism <span class="Math">\mathrm{MorphismFromTensorProductToInternalHomWithGivenObjects}_{a,b}: a^{\vee} \otimes b \rightarrow \mathrm{\underline{Hom}}(a,b)</span>.</p>

<p><a id="X8430726C82D6CFF7" name="X8430726C82D6CFF7"></a></p>

<h5>1.6-45 IsomorphismFromDualObjectToInternalHomIntoTensorUnit</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsomorphismFromDualObjectToInternalHomIntoTensorUnit</code>( <var class="Arg">a</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(a^{\vee}, \mathrm{\underline{Hom}}(a,1))</span>.</p>

<p>The argument is an object <span class="Math">a</span>. The output is the isomorphism <span class="Math">\mathrm{IsomorphismFromDualObjectToInternalHomIntoTensorUnit}_{a}: a^{\vee} \rightarrow \mathrm{\underline{Hom}}(a,1)</span>.</p>

<p><a id="X7A015736812A97C6" name="X7A015736812A97C6"></a></p>

<h5>1.6-46 IsomorphismFromInternalHomIntoTensorUnitToDualObject</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsomorphismFromInternalHomIntoTensorUnitToDualObject</code>( <var class="Arg">a</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(\mathrm{\underline{Hom}}(a,1), a^{\vee})</span>.</p>

<p>The argument is an object <span class="Math">a</span>. The output is the isomorphism <span class="Math">\mathrm{IsomorphismFromInternalHomIntoTensorUnitToDualObject}_{a}: \mathrm{\underline{Hom}}(a,1) \rightarrow a^{\vee}</span>.</p>

<p><a id="X7AF8F68887146C20" name="X7AF8F68887146C20"></a></p>

<h5>1.6-47 UniversalPropertyOfDual</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ UniversalPropertyOfDual</code>( <var class="Arg">t</var>, <var class="Arg">a</var>, <var class="Arg">alpha</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(t, a^{\vee})</span>.</p>

<p>The arguments are two objects <span class="Math">t,a</span>, and a morphism <span class="Math">\alpha: t \otimes a \rightarrow 1</span>. The output is the morphism <span class="Math">t \rightarrow a^{\vee}</span> given by the universal property of <span class="Math">a^{\vee}</span>.</p>

<p><a id="X80F3F2287B9E55E3" name="X80F3F2287B9E55E3"></a></p>

<h5>1.6-48 LambdaIntroduction</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LambdaIntroduction</code>( <var class="Arg">alpha</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( 1, \mathrm{\underline{Hom}}(a,b) )</span>.</p>

<p>The argument is a morphism <span class="Math">\alpha: a \rightarrow b</span>. The output is the corresponding morphism <span class="Math">1 \rightarrow \mathrm{\underline{Hom}}(a,b)</span> under the tensor hom adjunction.</p>

<p><a id="X79EC44077F661E80" name="X79EC44077F661E80"></a></p>

<h5>1.6-49 LambdaElimination</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LambdaElimination</code>( <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">alpha</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(a,b)</span>.</p>

<p>The arguments are two objects <span class="Math">a,b</span>, and a morphism <span class="Math">\alpha: 1 \rightarrow \mathrm{\underline{Hom}}(a,b)</span>. The output is a morphism <span class="Math">a \rightarrow b</span> corresponding to <span class="Math">\alpha</span> under the tensor hom adjunction.</p>

<p><a id="X8726BA888787D53D" name="X8726BA888787D53D"></a></p>

<h5>1.6-50 IsomorphismFromObjectToInternalHom</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsomorphismFromObjectToInternalHom</code>( <var class="Arg">a</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(a, \mathrm{\underline{Hom}}(1,a))</span>.</p>

<p>The argument is an object <span class="Math">a</span>. The output is the natural isomorphism <span class="Math">a \rightarrow \mathrm{\underline{Hom}}(1,a)</span>.</p>

<p><a id="X87F91EF37C76A7F7" name="X87F91EF37C76A7F7"></a></p>

<h5>1.6-51 IsomorphismFromObjectToInternalHomWithGivenInternalHom</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsomorphismFromObjectToInternalHomWithGivenInternalHom</code>( <var class="Arg">a</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(a, r)</span>.</p>

<p>The argument is an object <span class="Math">a</span>, and an object <span class="Math">r = \mathrm{\underline{Hom}}(1,a)</span>. The output is the natural isomorphism <span class="Math">a \rightarrow \mathrm{\underline{Hom}}(1,a)</span>.</p>

<p><a id="X831CF4E1824FA178" name="X831CF4E1824FA178"></a></p>

<h5>1.6-52 IsomorphismFromInternalHomToObject</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsomorphismFromInternalHomToObject</code>( <var class="Arg">a</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(\mathrm{\underline{Hom}}(1,a),a)</span>.</p>

<p>The argument is an object <span class="Math">a</span>. The output is the natural isomorphism <span class="Math">\mathrm{\underline{Hom}}(1,a) \rightarrow a</span>.</p>

<p><a id="X7988DC7C79BED3B2" name="X7988DC7C79BED3B2"></a></p>

<h5>1.6-53 IsomorphismFromInternalHomToObjectWithGivenInternalHom</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsomorphismFromInternalHomToObjectWithGivenInternalHom</code>( <var class="Arg">a</var>, <var class="Arg">s</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(s,a)</span>.</p>

<p>The argument is an object <span class="Math">a</span>, and an object <span class="Math">s = \mathrm{\underline{Hom}}(1,a)</span>. The output is the natural isomorphism <span class="Math">\mathrm{\underline{Hom}}(1,a) \rightarrow a</span>.</p>

<p><a id="X86546D277A535EB1" name="X86546D277A535EB1"></a></p>

<h4>1.7 <span class="Heading">Left Coclosed Monoidal Categories</span></h4>

<p>A monoidal category <span class="Math">\mathbf{C}</span> which has for each functor <span class="Math">- \otimes b: \mathbf{C} \rightarrow \mathbf{C}</span> a left adjoint (denoted by <span class="Math">\mathrm{\underline{coHom}}(-,b)</span>) is called a <em>left coclosed monoidal category</em>.</p>

<p>If no operations involving left coduals are installed manually, the left codual objects will be derived as <span class="Math">a_\vee \coloneqq \mathrm{\underline{coHom}}(1,a)</span>.</p>

<p>The corresponding GAP property is called <code class="code">IsLeftCoclosedMonoidalCategory</code>.</p>

<p><a id="X7CE5D10B7F10E9CC" name="X7CE5D10B7F10E9CC"></a></p>

<h5>1.7-1 LeftInternalCoHomOnObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftInternalCoHomOnObjects</code>( <var class="Arg">a</var>, <var class="Arg">b</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: an object</p>

<p>The arguments are two objects <span class="Math">a,b</span>. The output is the internal cohom object <span class="Math">\mathrm{\underline{coHom}_\ell}(a,b)</span>.</p>

<p><a id="X853213767BB48099" name="X853213767BB48099"></a></p>

<h5>1.7-2 LeftInternalCoHomOnMorphisms</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftInternalCoHomOnMorphisms</code>( <var class="Arg">alpha</var>, <var class="Arg">beta</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( \mathrm{\underline{coHom}_\ell}(a,b'), \mathrm{\underline{coHom}_\ell}(a',b) )</span></p>

<p>The arguments are two morphisms <span class="Math">\alpha: a \rightarrow a', \beta: b \rightarrow b'</span>. The output is the internal cohom morphism <span class="Math">\mathrm{\underline{coHom}_\ell}(\alpha,\beta): \mathrm{\underline{coHom}_\ell}(a,b') \rightarrow \mathrm{\underline{coHom}_\ell}(a',b)</span>.</p>

<p><a id="X7F302E3880752A2F" name="X7F302E3880752A2F"></a></p>

<h5>1.7-3 LeftInternalCoHomOnMorphismsWithGivenLeftInternalCoHoms</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftInternalCoHomOnMorphismsWithGivenLeftInternalCoHoms</code>( <var class="Arg">s</var>, <var class="Arg">alpha</var>, <var class="Arg">beta</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( s, r )</span></p>

<p>The arguments are an object <span class="Math">s = \mathrm{\underline{coHom}_\ell}(a,b')</span>, two morphisms <span class="Math">\alpha: a \rightarrow a', \beta: b \rightarrow b'</span>, and an object <span class="Math">r = \mathrm{\underline{coHom}_\ell}(a',b)</span>. The output is the internal cohom morphism <span class="Math">\mathrm{\underline{coHom}_\ell}(\alpha,\beta): \mathrm{\underline{coHom}_\ell}(a,b') \rightarrow \mathrm{\underline{coHom}_\ell}(a',b)</span>.</p>

<p><a id="X819A762D83B1C294" name="X819A762D83B1C294"></a></p>

<h5>1.7-4 LeftCoclosedMonoidalEvaluationMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftCoclosedMonoidalEvaluationMorphism</code>( <var class="Arg">a</var>, <var class="Arg">b</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( b, \mathrm{\underline{coHom}_\ell}(b,a) \otimes a )</span>.</p>

<p>The arguments are two objects <span class="Math">a, b</span>. The output is the coclosed evaluation morphism <span class="Math">\mathrm{coclev}_{a,b}: b \rightarrow \mathrm{\underline{coHom}_\ell}(b,a) \otimes a</span>, i.e., the unit of the cohom tensor adjunction.</p>

<p><a id="X7E5607B1789E00B7" name="X7E5607B1789E00B7"></a></p>

<h5>1.7-5 LeftCoclosedMonoidalEvaluationMorphismWithGivenRange</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftCoclosedMonoidalEvaluationMorphismWithGivenRange</code>( <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( b, r )</span>.</p>

<p>The arguments are two objects <span class="Math">a,b</span> and an object <span class="Math">r = \mathrm{\underline{coHom}_\ell}(b,a) \otimes a</span>. The output is the coclosed evaluation morphism <span class="Math">\mathrm{coclev}_{a,b}: b \rightarrow \mathrm{\underline{coHom}_\ell}(b,a) \otimes a</span>, i.e., the unit of the cohom tensor adjunction.</p>

<p><a id="X81A249CE84828A9D" name="X81A249CE84828A9D"></a></p>

<h5>1.7-6 LeftCoclosedMonoidalCoevaluationMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftCoclosedMonoidalCoevaluationMorphism</code>( <var class="Arg">a</var>, <var class="Arg">b</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( \mathrm{\underline{coHom}_\ell}(b \otimes a, a), b )</span>.</p>

<p>The arguments are two objects <span class="Math">a,b</span>. The output is the coclosed coevaluation morphism <span class="Math">\mathrm{coclcoev}_{a,b}: \mathrm{\underline{coHom}_\ell}(b \otimes a, a) \rightarrow b</span>, i.e., the counit of the cohom tensor adjunction.</p>

<p><a id="X7D1018A284F21140" name="X7D1018A284F21140"></a></p>

<h5>1.7-7 LeftCoclosedMonoidalCoevaluationMorphismWithGivenSource</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftCoclosedMonoidalCoevaluationMorphismWithGivenSource</code>( <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">s</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( s, b )</span>.</p>

<p>The arguments are two objects <span class="Math">a,b</span> and an object <span class="Math">s = \mathrm{\underline{coHom}_\ell}(b \otimes a, a)</span>. The output is the coclosed coevaluation morphism <span class="Math">\mathrm{coclcoev}_{a,b}: \mathrm{\underline{coHom}_\ell}(b \otimes a, a) \rightarrow b</span>, i.e., the unit of the cohom tensor adjunction.</p>

<p><a id="X851216B2807B3900" name="X851216B2807B3900"></a></p>

<h5>1.7-8 TensorProductToLeftInternalCoHomAdjunctMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TensorProductToLeftInternalCoHomAdjunctMorphism</code>( <var class="Arg">b</var>, <var class="Arg">c</var>, <var class="Arg">g</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( \mathrm{\underline{coHom}_\ell}(a,c), b )</span>.</p>

<p>The arguments are two objects <span class="Math">b,c</span> and a morphism <span class="Math">g: a \rightarrow b \otimes c</span>. The output is a morphism <span class="Math">f: \mathrm{\underline{coHom}_\ell}(a,c) \rightarrow b</span> corresponding to <span class="Math">g</span> under the cohom tensor adjunction.</p>

<p><a id="X87BFA0FA7AFF2868" name="X87BFA0FA7AFF2868"></a></p>

<h5>1.7-9 TensorProductToLeftInternalCoHomAdjunctMorphismWithGivenLeftInternalCoHom</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TensorProductToLeftInternalCoHomAdjunctMorphismWithGivenLeftInternalCoHom</code>( <var class="Arg">b</var>, <var class="Arg">c</var>, <var class="Arg">g</var>, <var class="Arg">i</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( i, b )</span>.</p>

<p>The arguments are two objects <span class="Math">b,c</span>, a morphism <span class="Math">g: a \rightarrow b \otimes c</span> and an object <span class="Math">i = \mathrm{\underline{coHom}_\ell}(a,c)</span>. The output is a morphism <span class="Math">f: \mathrm{\underline{coHom}_\ell}(a,c) \rightarrow b</span> corresponding to <span class="Math">g</span> under the cohom tensor adjunction.</p>

<p><a id="X7DDDACD58454C3A4" name="X7DDDACD58454C3A4"></a></p>

<h5>1.7-10 LeftInternalCoHomToTensorProductAdjunctMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftInternalCoHomToTensorProductAdjunctMorphism</code>( <var class="Arg">a</var>, <var class="Arg">c</var>, <var class="Arg">f</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(a, b \otimes c)</span>.</p>

<p>The arguments are two objects <span class="Math">a,c</span> and a morphism <span class="Math">f: \mathrm{\underline{coHom}_\ell}(a,c) \rightarrow b</span>. The output is a morphism <span class="Math">g: a \rightarrow b \otimes c</span> corresponding to <span class="Math">f</span> under the cohom tensor adjunction.</p>

<p><a id="X821AC96981CA794C" name="X821AC96981CA794C"></a></p>

<h5>1.7-11 LeftInternalCoHomToTensorProductAdjunctMorphismWithGivenTensorProduct</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftInternalCoHomToTensorProductAdjunctMorphismWithGivenTensorProduct</code>( <var class="Arg">a</var>, <var class="Arg">c</var>, <var class="Arg">f</var>, <var class="Arg">t</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( a, t )</span>.</p>

<p>The arguments are two objects <span class="Math">a,c</span>, a morphism <span class="Math">f: \mathrm{\underline{coHom}_\ell}(a,c) \rightarrow b</span> and an object <span class="Math">t = b \otimes c</span>. The output is a morphism <span class="Math">g: a \rightarrow b \otimes c</span> corresponding to <span class="Math">f</span> under the cohom tensor adjunction.</p>

<p><a id="X8416357982DCBEE4" name="X8416357982DCBEE4"></a></p>

<h5>1.7-12 LeftCoclosedMonoidalPreCoComposeMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftCoclosedMonoidalPreCoComposeMorphism</code>( <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">c</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( \mathrm{\underline{coHom}_\ell}(a,c), \mathrm{\underline{coHom}_\ell}(b,c) \otimes \mathrm{\underline{coHom}_\ell}(a,b) )</span>.</p>

<p>The arguments are three objects <span class="Math">a,b,c</span>. The output is the precocomposition morphism <span class="Math">\mathrm{LeftCoclosedMonoidalPreCoComposeMorphism}_{a,b,c}: \mathrm{\underline{coHom}_\ell}(a,c) \rightarrow \mathrm{\underline{coHom}_\ell}(b,c) \otimes \mathrm{\underline{coHom}_\ell}(a,b)</span>.</p>

<p><a id="X7EECDE4583E14A59" name="X7EECDE4583E14A59"></a></p>

<h5>1.7-13 LeftCoclosedMonoidalPreCoComposeMorphismWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftCoclosedMonoidalPreCoComposeMorphismWithGivenObjects</code>( <var class="Arg">s</var>, <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">c</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( s, r )</span>.</p>

<p>The arguments are an object <span class="Math">s = \mathrm{\underline{coHom}_\ell}(a,c)</span>, three objects <span class="Math">a,b,c</span>, and an object <span class="Math">r = \mathrm{\underline{coHom}_\ell}(a,b) \otimes \mathrm{\underline{coHom}_\ell}(b,c)</span>. The output is the precocomposition morphism <span class="Math">\mathrm{LeftCoclosedMonoidalPreCoComposeMorphismWithGivenObjects}_{a,b,c}: \mathrm{\underline{coHom}_\ell}(a,c) \rightarrow \mathrm{\underline{coHom}_\ell}(b,c) \otimes \mathrm{\underline{coHom}_\ell}(a,b)</span>.</p>

<p><a id="X80A270E982F5BC2D" name="X80A270E982F5BC2D"></a></p>

<h5>1.7-14 LeftCoclosedMonoidalPostCoComposeMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftCoclosedMonoidalPostCoComposeMorphism</code>( <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">c</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( \mathrm{\underline{coHom}_\ell}(a,c), \mathrm{\underline{coHom}_\ell}(a,b) \otimes \mathrm{\underline{coHom}_\ell}(b,c) )</span>.</p>

<p>The arguments are three objects <span class="Math">a,b,c</span>. The output is the postcocomposition morphism <span class="Math">\mathrm{LeftCoclosedMonoidalPostCoComposeMorphism}_{a,b,c}: \mathrm{\underline{coHom}_\ell}(a,c) \rightarrow \mathrm{\underline{coHom}_\ell}(a,b) \otimes \mathrm{\underline{coHom}_\ell}(b,c)</span>.</p>

<p><a id="X867C6F087D72AB3F" name="X867C6F087D72AB3F"></a></p>

<h5>1.7-15 LeftCoclosedMonoidalPostCoComposeMorphismWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftCoclosedMonoidalPostCoComposeMorphismWithGivenObjects</code>( <var class="Arg">s</var>, <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">c</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( s, r )</span>.</p>

<p>The arguments are an object <span class="Math">s = \mathrm{\underline{coHom}_\ell}(a,c)</span>, three objects <span class="Math">a,b,c</span>, and an object <span class="Math">r = \mathrm{\underline{coHom}_\ell}(b,c) \otimes \mathrm{\underline{coHom}_\ell}(a,b)</span>. The output is the postcocomposition morphism <span class="Math">\mathrm{LeftCoclosedMonoidalPostCoComposeMorphismWithGivenObjects}_{a,b,c}: \mathrm{\underline{coHom}_\ell}(a,c) \rightarrow \mathrm{\underline{coHom}_\ell}(a,b) \otimes \mathrm{\underline{coHom}_\ell}(b,c)</span>.</p>

<p><a id="X85A63AA57F0678EE" name="X85A63AA57F0678EE"></a></p>

<h5>1.7-16 LeftCoDualOnObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftCoDualOnObjects</code>( <var class="Arg">a</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: an object</p>

<p>The argument is an object <span class="Math">a</span>. The output is its codual object <span class="Math">a_{\vee}</span>.</p>

<p><a id="X7949DE307D2D5083" name="X7949DE307D2D5083"></a></p>

<h5>1.7-17 LeftCoDualOnMorphisms</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftCoDualOnMorphisms</code>( <var class="Arg">alpha</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( b_{\vee}, a_{\vee} )</span>.</p>

<p>The argument is a morphism <span class="Math">\alpha: a \rightarrow b</span>. The output is its codual morphism <span class="Math">\alpha_{\vee}: b_{\vee} \rightarrow a_{\vee}</span>.</p>

<p><a id="X84C835CB7E708596" name="X84C835CB7E708596"></a></p>

<h5>1.7-18 LeftCoDualOnMorphismsWithGivenLeftCoDuals</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftCoDualOnMorphismsWithGivenLeftCoDuals</code>( <var class="Arg">s</var>, <var class="Arg">alpha</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( s, r )</span>.</p>

<p>The argument is an object <span class="Math">s = b_{\vee}</span>, a morphism <span class="Math">\alpha: a \rightarrow b</span>, and an object <span class="Math">r = a_{\vee}</span>. The output is the dual morphism <span class="Math">\alpha_{\vee}: b^{\vee} \rightarrow a^{\vee}</span>.</p>

<p><a id="X7A20AC6A837F79BA" name="X7A20AC6A837F79BA"></a></p>

<h5>1.7-19 LeftCoclosedMonoidalEvaluationForLeftCoDual</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftCoclosedMonoidalEvaluationForLeftCoDual</code>( <var class="Arg">a</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( 1, a_{\vee} \otimes a )</span>.</p>

<p>The argument is an object <span class="Math">a</span>. The output is the coclosed evaluation morphism <span class="Math">\mathrm{coclev}_{a}: 1 \rightarrow a_{\vee} \otimes a</span>.</p>

<p><a id="X87B15AC678955783" name="X87B15AC678955783"></a></p>

<h5>1.7-20 LeftCoclosedMonoidalEvaluationForLeftCoDualWithGivenTensorProduct</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftCoclosedMonoidalEvaluationForLeftCoDualWithGivenTensorProduct</code>( <var class="Arg">s</var>, <var class="Arg">a</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( s, r )</span>.</p>

<p>The arguments are an object <span class="Math">s = 1</span>, an object <span class="Math">a</span>, and an object <span class="Math">r = a_{\vee} \otimes a</span>. The output is the coclosed evaluation morphism <span class="Math">\mathrm{coclev}_{a}: 1 \rightarrow a_{\vee} \otimes a</span>.</p>

<p><a id="X7F67676A85A47BDB" name="X7F67676A85A47BDB"></a></p>

<h5>1.7-21 MorphismFromLeftCoBidual</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ MorphismFromLeftCoBidual</code>( <var class="Arg">a</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}((a_{\vee})_{\vee}, a)</span>.</p>

<p>The argument is an object <span class="Math">a</span>. The output is the morphism from the cobidual <span class="Math">(a_{\vee})_{\vee} \rightarrow a</span>.</p>

<p><a id="X7AF5F77180E09AAE" name="X7AF5F77180E09AAE"></a></p>

<h5>1.7-22 MorphismFromLeftCoBidualWithGivenLeftCoBidual</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ MorphismFromLeftCoBidualWithGivenLeftCoBidual</code>( <var class="Arg">a</var>, <var class="Arg">s</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(s, a)</span>.</p>

<p>The arguments are an object <span class="Math">a</span>, and an object <span class="Math">s = (a_{\vee})_{\vee}</span>. The output is the morphism from the cobidual <span class="Math">(a_{\vee})_{\vee} \rightarrow a</span>.</p>

<p><a id="X84331A1B7F62782F" name="X84331A1B7F62782F"></a></p>

<h5>1.7-23 LeftInternalCoHomTensorProductCompatibilityMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftInternalCoHomTensorProductCompatibilityMorphism</code>( <var class="Arg">list</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( \mathrm{\underline{coHom}_\ell}(a \otimes a', b \otimes b'), \mathrm{\underline{coHom}_\ell}(a,b) \otimes \mathrm{\underline{coHom}_\ell}(a',b'))</span>.</p>

<p>The argument is a list of four objects <span class="Math">[ a, a', b, b' ]</span>. The output is the natural morphism <span class="Math">\mathrm{LeftInternalCoHomTensorProductCompatibilityMorphism}_{a,a',b,b'}: \mathrm{\underline{coHom}_\ell}(a \otimes a', b \otimes b') \rightarrow \mathrm{\underline{coHom}_\ell}(a,b) \otimes \mathrm{\underline{coHom}_\ell}(a',b')</span>.</p>

<p><a id="X808BEB0879D58CAF" name="X808BEB0879D58CAF"></a></p>

<h5>1.7-24 LeftInternalCoHomTensorProductCompatibilityMorphismWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftInternalCoHomTensorProductCompatibilityMorphismWithGivenObjects</code>( <var class="Arg">s</var>, <var class="Arg">list</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( s, r )</span>.</p>

<p>The arguments are a list of four objects <span class="Math">[ a, a', b, b' ]</span>, and two objects <span class="Math">s = \mathrm{\underline{coHom}_\ell}(a \otimes a', b \otimes b')</span> and <span class="Math">r = \mathrm{\underline{coHom}_\ell}(a,b) \otimes \mathrm{\underline{coHom}_\ell}(a',b')</span>. The output is the natural morphism <span class="Math">\mathrm{LeftInternalCoHomTensorProductCompatibilityMorphismWithGivenObjects}_{a,a',b,b'}: \mathrm{\underline{coHom}_\ell}(a \otimes a', b \otimes b') \rightarrow \mathrm{\underline{coHom}_\ell}(a,b) \otimes \mathrm{\underline{coHom}_\ell}(a',b')</span>.</p>

<p><a id="X7B4A66A8803C99BA" name="X7B4A66A8803C99BA"></a></p>

<h5>1.7-25 LeftCoDualityTensorProductCompatibilityMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftCoDualityTensorProductCompatibilityMorphism</code>( <var class="Arg">a</var>, <var class="Arg">b</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( (a \otimes b)_{\vee}, a_{\vee} \otimes b_{\vee} )</span>.</p>

<p>The arguments are two objects <span class="Math">a,b</span>. The output is the natural morphism <span class="Math">\mathrm{LeftCoDualityTensorProductCompatibilityMorphism}: (a \otimes b)_{\vee} \rightarrow a_{\vee} \otimes b_{\vee}</span>.</p>

<p><a id="X86E72092788A8F2D" name="X86E72092788A8F2D"></a></p>

<h5>1.7-26 LeftCoDualityTensorProductCompatibilityMorphismWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftCoDualityTensorProductCompatibilityMorphismWithGivenObjects</code>( <var class="Arg">s</var>, <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( s, r )</span>.</p>

<p>The arguments are an object <span class="Math">s = (a \otimes b)_{\vee}</span>, two objects <span class="Math">a,b</span>, and an object <span class="Math">r = a_{\vee} \otimes b_{\vee}</span>. The output is the natural morphism <span class="Math">\mathrm{LeftCoDualityTensorProductCompatibilityMorphismWithGivenObjects}_{a,b}: (a \otimes b)_{\vee} \rightarrow a_{\vee} \otimes b_{\vee}</span>.</p>

<p><a id="X7A5FDE4B83C5F328" name="X7A5FDE4B83C5F328"></a></p>

<h5>1.7-27 MorphismFromLeftInternalCoHomToTensorProduct</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ MorphismFromLeftInternalCoHomToTensorProduct</code>( <var class="Arg">a</var>, <var class="Arg">b</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( \mathrm{\underline{coHom}_\ell}(a,b), b_{\vee} \otimes a )</span>.</p>

<p>The arguments are two objects <span class="Math">a,b</span>. The output is the natural morphism <span class="Math">\mathrm{MorphismFromLeftInternalCoHomToTensorProduct}_{a,b}: \mathrm{\underline{coHom}_\ell}(a,b) \rightarrow b_{\vee} \otimes a</span>.</p>

<p><a id="X7BD2A33F84A2FBAB" name="X7BD2A33F84A2FBAB"></a></p>

<h5>1.7-28 MorphismFromLeftInternalCoHomToTensorProductWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ MorphismFromLeftInternalCoHomToTensorProductWithGivenObjects</code>( <var class="Arg">s</var>, <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( s, r )</span>.</p>

<p>The arguments are an object <span class="Math">s = \mathrm{\underline{coHom}_\ell}(a,b)</span>, two objects <span class="Math">a,b</span>, and an object <span class="Math">r = b_{\vee} \otimes a</span>. The output is the natural morphism <span class="Math">\mathrm{MorphismFromLeftInternalCoHomToTensorProductWithGivenObjects}_{a,b}: \mathrm{\underline{coHom}_\ell}(a,b) \rightarrow a \otimes b_{\vee}</span>.</p>

<p><a id="X7CC10C9E7EA7EED4" name="X7CC10C9E7EA7EED4"></a></p>

<h5>1.7-29 IsomorphismFromLeftCoDualObjectToLeftInternalCoHomFromTensorUnit</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsomorphismFromLeftCoDualObjectToLeftInternalCoHomFromTensorUnit</code>( <var class="Arg">a</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(a_{\vee}, \mathrm{\underline{coHom}_\ell}(1,a))</span>.</p>

<p>The argument is an object <span class="Math">a</span>. The output is the isomorphism <span class="Math">\mathrm{IsomorphismFromLeftCoDualObjectToLeftInternalCoHomFromTensorUnit}_{a}: a_{\vee} \rightarrow \mathrm{\underline{coHom}_\ell}(1,a)</span>.</p>

<p><a id="X87F96B047F320A17" name="X87F96B047F320A17"></a></p>

<h5>1.7-30 IsomorphismFromLeftInternalCoHomFromTensorUnitToLeftCoDualObject</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsomorphismFromLeftInternalCoHomFromTensorUnitToLeftCoDualObject</code>( <var class="Arg">a</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(\mathrm{\underline{coHom}_\ell}(1,a), a_{\vee})</span>.</p>

<p>The argument is an object <span class="Math">a</span>. The output is the isomorphism <span class="Math">\mathrm{IsomorphismFromLeftInternalCoHomFromTensorUnitToLeftCoDualObject}_{a}: \mathrm{\underline{coHom}_\ell}(1,a) \rightarrow a_{\vee}</span>.</p>

<p><a id="X7A0DE1667FF28457" name="X7A0DE1667FF28457"></a></p>

<h5>1.7-31 UniversalPropertyOfLeftCoDual</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ UniversalPropertyOfLeftCoDual</code>( <var class="Arg">t</var>, <var class="Arg">a</var>, <var class="Arg">alpha</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(a_{\vee}, t)</span>.</p>

<p>The arguments are two objects <span class="Math">t,a</span>, and a morphism <span class="Math">\alpha: 1 \rightarrow t \otimes a</span>. The output is the morphism <span class="Math">a_{\vee} \rightarrow t</span> given by the universal property of <span class="Math">a_{\vee}</span>.</p>

<p><a id="X85960F7479FFA8DA" name="X85960F7479FFA8DA"></a></p>

<h5>1.7-32 LeftCoclosedMonoidalLambdaIntroduction</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftCoclosedMonoidalLambdaIntroduction</code>( <var class="Arg">alpha</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( \mathrm{\underline{coHom}_\ell}(a,b), 1 )</span>.</p>

<p>The argument is a morphism <span class="Math">\alpha: a \rightarrow b</span>. The output is the corresponding morphism <span class="Math"> \mathrm{\underline{coHom}_\ell}(a,b) \rightarrow 1</span> under the cohom tensor adjunction.</p>

<p><a id="X8721DDEC7DF9D89D" name="X8721DDEC7DF9D89D"></a></p>

<h5>1.7-33 LeftCoclosedMonoidalLambdaElimination</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftCoclosedMonoidalLambdaElimination</code>( <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">alpha</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(a,b)</span>.</p>

<p>The arguments are two objects <span class="Math">a,b</span>, and a morphism <span class="Math">\alpha: \mathrm{\underline{coHom}_\ell}(a,b) \rightarrow 1</span>. The output is a morphism <span class="Math">a \rightarrow b</span> corresponding to <span class="Math">\alpha</span> under the cohom tensor adjunction.</p>

<p><a id="X853342457CC3B489" name="X853342457CC3B489"></a></p>

<h5>1.7-34 IsomorphismFromObjectToLeftInternalCoHom</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsomorphismFromObjectToLeftInternalCoHom</code>( <var class="Arg">a</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(a, \mathrm{\underline{coHom}_\ell}(a,1))</span>.</p>

<p>The argument is an object <span class="Math">a</span>. The output is the natural isomorphism <span class="Math">a \rightarrow \mathrm{\underline{coHom}_\ell}(a,1)</span>.</p>

<p><a id="X82709BED807CB6FC" name="X82709BED807CB6FC"></a></p>

<h5>1.7-35 IsomorphismFromObjectToLeftInternalCoHomWithGivenLeftInternalCoHom</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsomorphismFromObjectToLeftInternalCoHomWithGivenLeftInternalCoHom</code>( <var class="Arg">a</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(a, r)</span>.</p>

<p>The argument is an object <span class="Math">a</span>, and an object <span class="Math">r = \mathrm{\underline{coHom}_\ell}(a,1)</span>. The output is the natural isomorphism <span class="Math">a \rightarrow \mathrm{\underline{coHom}_\ell}(a,1)</span>.</p>

<p><a id="X806C843B82108148" name="X806C843B82108148"></a></p>

<h5>1.7-36 IsomorphismFromLeftInternalCoHomToObject</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsomorphismFromLeftInternalCoHomToObject</code>( <var class="Arg">a</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(\mathrm{\underline{coHom}_\ell}(a,1), a)</span>.</p>

<p>The argument is an object <span class="Math">a</span>. The output is the natural isomorphism <span class="Math">\mathrm{\underline{coHom}_\ell}(a,1) \rightarrow a</span>.</p>

<p><a id="X8370164B7EAF833D" name="X8370164B7EAF833D"></a></p>

<h5>1.7-37 IsomorphismFromLeftInternalCoHomToObjectWithGivenLeftInternalCoHom</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsomorphismFromLeftInternalCoHomToObjectWithGivenLeftInternalCoHom</code>( <var class="Arg">a</var>, <var class="Arg">s</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(s, a)</span>.</p>

<p>The argument is an object <span class="Math">a</span>, and an object <span class="Math">s = \mathrm{\underline{coHom}_\ell}(a,1)</span>. The output is the natural isomorphism <span class="Math">\mathrm{\underline{coHom}_\ell}(a,1) \rightarrow a</span>.</p>

<p><a id="X8197D69B805349AC" name="X8197D69B805349AC"></a></p>

<h4>1.8 <span class="Heading">Coclosed Monoidal Categories</span></h4>

<p>A monoidal category <span class="Math">\mathbf{C}</span> which has for each functor <span class="Math">- \otimes b: \mathbf{C} \rightarrow \mathbf{C}</span> a left adjoint (denoted by <span class="Math">\mathrm{\underline{coHom}}(-,b)</span>) is called a <em>coclosed monoidal category</em>.</p>

<p>If no operations involving coduals are installed manually, the codual objects will be derived as <span class="Math">a_\vee \coloneqq \mathrm{\underline{coHom}}(1,a)</span>.</p>

<p>The corresponding GAP property is called <code class="code">IsCoclosedMonoidalCategory</code>.</p>

<p><a id="X791BE0B0847A430D" name="X791BE0B0847A430D"></a></p>

<h5>1.8-1 InternalCoHomOnObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ InternalCoHomOnObjects</code>( <var class="Arg">a</var>, <var class="Arg">b</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: an object</p>

<p>The arguments are two objects <span class="Math">a,b</span>. The output is the internal cohom object <span class="Math">\mathrm{\underline{coHom}}(a,b)</span>.</p>

<p><a id="X7FDF105D7F56EB53" name="X7FDF105D7F56EB53"></a></p>

<h5>1.8-2 InternalCoHomOnMorphisms</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ InternalCoHomOnMorphisms</code>( <var class="Arg">alpha</var>, <var class="Arg">beta</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( \mathrm{\underline{coHom}}(a,b'), \mathrm{\underline{coHom}}(a',b) )</span></p>

<p>The arguments are two morphisms <span class="Math">\alpha: a \rightarrow a', \beta: b \rightarrow b'</span>. The output is the internal cohom morphism <span class="Math">\mathrm{\underline{coHom}}(\alpha,\beta): \mathrm{\underline{coHom}}(a,b') \rightarrow \mathrm{\underline{coHom}}(a',b)</span>.</p>

<p><a id="X84DDA3DD878162B9" name="X84DDA3DD878162B9"></a></p>

<h5>1.8-3 InternalCoHomOnMorphismsWithGivenInternalCoHoms</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ InternalCoHomOnMorphismsWithGivenInternalCoHoms</code>( <var class="Arg">s</var>, <var class="Arg">alpha</var>, <var class="Arg">beta</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( s, r )</span></p>

<p>The arguments are an object <span class="Math">s = \mathrm{\underline{coHom}}(a,b')</span>, two morphisms <span class="Math">\alpha: a \rightarrow a', \beta: b \rightarrow b'</span>, and an object <span class="Math">r = \mathrm{\underline{coHom}}(a',b)</span>. The output is the internal cohom morphism <span class="Math">\mathrm{\underline{coHom}}(\alpha,\beta): \mathrm{\underline{coHom}}(a,b') \rightarrow \mathrm{\underline{coHom}}(a',b)</span>.</p>

<p><a id="X83CEC88D79AE5684" name="X83CEC88D79AE5684"></a></p>

<h5>1.8-4 CoclosedMonoidalRightEvaluationMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ CoclosedMonoidalRightEvaluationMorphism</code>( <var class="Arg">a</var>, <var class="Arg">b</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( b, a \otimes \mathrm{\underline{coHom}}(b,a) )</span>.</p>

<p>The arguments are two objects <span class="Math">a, b</span>. The output is the coclosed right evaluation morphism <span class="Math">\mathrm{coclev}_{a,b}: b \rightarrow a \otimes \mathrm{\underline{coHom}}(b,a)</span>, i.e., the unit of the cohom tensor adjunction.</p>

<p><a id="X79333EC9822EA316" name="X79333EC9822EA316"></a></p>

<h5>1.8-5 CoclosedMonoidalRightEvaluationMorphismWithGivenRange</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ CoclosedMonoidalRightEvaluationMorphismWithGivenRange</code>( <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( b, r )</span>.</p>

<p>The arguments are two objects <span class="Math">a,b</span> and an object <span class="Math">r = a \otimes \mathrm{\underline{coHom}}(b,a)</span>. The output is the coclosed right evaluation morphism <span class="Math">\mathrm{coclev}_{a,b}: b \rightarrow a \otimes \mathrm{\underline{coHom}}(b,a)</span>, i.e., the unit of the cohom tensor adjunction.</p>

<p><a id="X80CA11547F3909E3" name="X80CA11547F3909E3"></a></p>

<h5>1.8-6 CoclosedMonoidalRightCoevaluationMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ CoclosedMonoidalRightCoevaluationMorphism</code>( <var class="Arg">a</var>, <var class="Arg">b</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( \mathrm{\underline{coHom}}(a \otimes b, a), b )</span>.</p>

<p>The arguments are two objects <span class="Math">a,b</span>. The output is the coclosed right coevaluation morphism <span class="Math">\mathrm{coclcoev}_{a,b}: \mathrm{\underline{coHom}}(a \otimes b, a) \rightarrow b</span>, i.e., the counit of the cohom tensor adjunction.</p>

<p><a id="X7F1C10897EC4D14E" name="X7F1C10897EC4D14E"></a></p>

<h5>1.8-7 CoclosedMonoidalRightCoevaluationMorphismWithGivenSource</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ CoclosedMonoidalRightCoevaluationMorphismWithGivenSource</code>( <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">s</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( s, b )</span>.</p>

<p>The arguments are two objects <span class="Math">a,b</span> and an object <span class="Math">s = \mathrm{\underline{coHom}}(a \otimes b, a)</span>. The output is the coclosed right coevaluation morphism <span class="Math">\mathrm{coclcoev}_{a,b}: \mathrm{\underline{coHom}}(a \otimes b, a) \rightarrow b</span>, i.e., the unit of the cohom tensor adjunction.</p>

<p><a id="X82B0937678F04730" name="X82B0937678F04730"></a></p>

<h5>1.8-8 TensorProductToInternalCoHomRightAdjunctMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TensorProductToInternalCoHomRightAdjunctMorphism</code>( <var class="Arg">b</var>, <var class="Arg">c</var>, <var class="Arg">g</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( \mathrm{\underline{coHom}}(a,b), c )</span>.</p>

<p>The arguments are two objects <span class="Math">b,c</span> and a morphism <span class="Math">g: a \rightarrow b \otimes c</span>. The output is a morphism <span class="Math">f: \mathrm{\underline{coHom}}(a,b) \rightarrow c</span> corresponding to <span class="Math">g</span> under the cohom tensor adjunction.</p>

<p><a id="X833D7B567810D7F3" name="X833D7B567810D7F3"></a></p>

<h5>1.8-9 TensorProductToInternalCoHomRightAdjunctMorphismWithGivenInternalCoHom</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TensorProductToInternalCoHomRightAdjunctMorphismWithGivenInternalCoHom</code>( <var class="Arg">b</var>, <var class="Arg">c</var>, <var class="Arg">g</var>, <var class="Arg">i</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( i, c )</span>.</p>

<p>The arguments are two objects <span class="Math">b,c</span>, a morphism <span class="Math">g: a \rightarrow b \otimes c</span> and an object <span class="Math">i = \mathrm{\underline{coHom}}(a,b)</span>. The output is a morphism <span class="Math">f: \mathrm{\underline{coHom}}(a,b) \rightarrow c</span> corresponding to <span class="Math">g</span> under the cohom tensor adjunction.</p>

<p><a id="X8623CC567D687FFD" name="X8623CC567D687FFD"></a></p>

<h5>1.8-10 InternalCoHomToTensorProductRightAdjunctMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ InternalCoHomToTensorProductRightAdjunctMorphism</code>( <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">f</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(a, b \otimes c)</span>.</p>

<p>The arguments are two objects <span class="Math">a,b</span> and a morphism <span class="Math">f: \mathrm{\underline{coHom}}(a,b) \rightarrow c</span>. The output is a morphism <span class="Math">g: a \rightarrow b \otimes c</span> corresponding to <span class="Math">f</span> under the cohom tensor adjunction.</p>

<p><a id="X821B5212835BD1F6" name="X821B5212835BD1F6"></a></p>

<h5>1.8-11 InternalCoHomToTensorProductRightAdjunctMorphismWithGivenTensorProduct</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ InternalCoHomToTensorProductRightAdjunctMorphismWithGivenTensorProduct</code>( <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">f</var>, <var class="Arg">t</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( a, t )</span>.</p>

<p>The arguments are two objects <span class="Math">a,b</span>, a morphism <span class="Math">f: \mathrm{\underline{coHom}}(a,b) \rightarrow c</span> and an object <span class="Math">t = b \otimes c</span>. The output is a morphism <span class="Math">g: a \rightarrow t</span> corresponding to <span class="Math">f</span> under the cohom tensor adjunction.</p>

<p><a id="X81020D9E85C3280A" name="X81020D9E85C3280A"></a></p>

<h5>1.8-12 CoclosedMonoidalLeftEvaluationMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ CoclosedMonoidalLeftEvaluationMorphism</code>( <var class="Arg">a</var>, <var class="Arg">b</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( b, \mathrm{\underline{coHom}}(b,a) \otimes a )</span>.</p>

<p>The arguments are two objects <span class="Math">a, b</span>. The output is the coclosed left evaluation morphism <span class="Math">\mathrm{coclev}_{a,b}: b \rightarrow \mathrm{\underline{coHom}}(b,a) \otimes a</span>, i.e., the unit of the cohom tensor adjunction.</p>

<p><a id="X7A1801D77EECEA29" name="X7A1801D77EECEA29"></a></p>

<h5>1.8-13 CoclosedMonoidalLeftEvaluationMorphismWithGivenRange</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ CoclosedMonoidalLeftEvaluationMorphismWithGivenRange</code>( <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( b, r )</span>.</p>

<p>The arguments are two objects <span class="Math">a,b</span> and an object <span class="Math">r = \mathrm{\underline{coHom}}(b,a) \otimes a</span>. The output is the coclosed left evaluation morphism <span class="Math">\mathrm{coclev}_{a,b}: b \rightarrow \mathrm{\underline{coHom}}(b,a) \otimes a</span>, i.e., the unit of the cohom tensor adjunction.</p>

<p><a id="X7D6905F582F06003" name="X7D6905F582F06003"></a></p>

<h5>1.8-14 CoclosedMonoidalLeftCoevaluationMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ CoclosedMonoidalLeftCoevaluationMorphism</code>( <var class="Arg">a</var>, <var class="Arg">b</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( \mathrm{\underline{coHom}}(b \otimes a, a), b )</span>.</p>

<p>The arguments are two objects <span class="Math">a,b</span>. The output is the coclosed left coevaluation morphism <span class="Math">\mathrm{coclcoev}_{a,b}: \mathrm{\underline{coHom}}(b \otimes a, a) \rightarrow b</span>, i.e., the counit of the cohom tensor adjunction.</p>

<p><a id="X802A3FC48280FBDE" name="X802A3FC48280FBDE"></a></p>

<h5>1.8-15 CoclosedMonoidalLeftCoevaluationMorphismWithGivenSource</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ CoclosedMonoidalLeftCoevaluationMorphismWithGivenSource</code>( <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">s</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( s, b )</span>.</p>

<p>The arguments are two objects <span class="Math">a,b</span> and an object <span class="Math">s = \mathrm{\underline{coHom}}(b \otimes a, a)</span>. The output is the coclosed left coevaluation morphism <span class="Math">\mathrm{coclcoev}_{a,b}: \mathrm{\underline{coHom}}(b \otimes a, a) \rightarrow b</span>, i.e., the unit of the cohom tensor adjunction.</p>

<p><a id="X7FB4953B7F813D0B" name="X7FB4953B7F813D0B"></a></p>

<h5>1.8-16 TensorProductToInternalCoHomLeftAdjunctMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TensorProductToInternalCoHomLeftAdjunctMorphism</code>( <var class="Arg">b</var>, <var class="Arg">c</var>, <var class="Arg">g</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( \mathrm{\underline{coHom}}(a,c), b )</span>.</p>

<p>The arguments are two objects <span class="Math">b,c</span> and a morphism <span class="Math">g: a \rightarrow b \otimes c</span>. The output is a morphism <span class="Math">f: \mathrm{\underline{coHom}}(a,c) \rightarrow b</span> corresponding to <span class="Math">g</span> under the cohom tensor adjunction.</p>

<p><a id="X8312DB0A82A97D4B" name="X8312DB0A82A97D4B"></a></p>

<h5>1.8-17 TensorProductToInternalCoHomLeftAdjunctMorphismWithGivenInternalCoHom</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TensorProductToInternalCoHomLeftAdjunctMorphismWithGivenInternalCoHom</code>( <var class="Arg">b</var>, <var class="Arg">c</var>, <var class="Arg">g</var>, <var class="Arg">i</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( i, b )</span>.</p>

<p>The arguments are two objects <span class="Math">b,c</span>, a morphism <span class="Math">g: a \rightarrow b \otimes c</span> and an object <span class="Math">i = \mathrm{\underline{coHom}}(a,c)</span>. The output is a morphism <span class="Math">f: \mathrm{\underline{coHom}}(a,c) \rightarrow b</span> corresponding to <span class="Math">g</span> under the cohom tensor adjunction.</p>

<p><a id="X7A7FC1957A1905C6" name="X7A7FC1957A1905C6"></a></p>

<h5>1.8-18 InternalCoHomToTensorProductLeftAdjunctMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ InternalCoHomToTensorProductLeftAdjunctMorphism</code>( <var class="Arg">a</var>, <var class="Arg">c</var>, <var class="Arg">f</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(a, b \otimes c)</span>.</p>

<p>The arguments are two objects <span class="Math">a,c</span> and a morphism <span class="Math">f: \mathrm{\underline{coHom}}(a,c) \rightarrow b</span>. The output is a morphism <span class="Math">g: a \rightarrow b \otimes c</span> corresponding to <span class="Math">f</span> under the cohom tensor adjunction.</p>

<p><a id="X85F970897F87BF2E" name="X85F970897F87BF2E"></a></p>

<h5>1.8-19 InternalCoHomToTensorProductLeftAdjunctMorphismWithGivenTensorProduct</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ InternalCoHomToTensorProductLeftAdjunctMorphismWithGivenTensorProduct</code>( <var class="Arg">a</var>, <var class="Arg">c</var>, <var class="Arg">f</var>, <var class="Arg">t</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( a, t )</span>.</p>

<p>The arguments are two objects <span class="Math">a,c</span>, a morphism <span class="Math">f: \mathrm{\underline{coHom}}(a,c) \rightarrow b</span> and an object <span class="Math">t = b \otimes c</span>. The output is a morphism <span class="Math">g: a \rightarrow t</span> corresponding to <span class="Math">f</span> under the cohom tensor adjunction.</p>

<p><a id="X8337DE6B7D61EAC2" name="X8337DE6B7D61EAC2"></a></p>

<h5>1.8-20 MonoidalPreCoComposeMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ MonoidalPreCoComposeMorphism</code>( <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">c</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( \mathrm{\underline{coHom}}(a,c), \mathrm{\underline{coHom}}(b,c) \otimes \mathrm{\underline{coHom}}(a,b) )</span>.</p>

<p>The arguments are three objects <span class="Math">a,b,c</span>. The output is the precocomposition morphism <span class="Math">\mathrm{MonoidalPreCoComposeMorphism}_{a,b,c}: \mathrm{\underline{coHom}}(a,c) \rightarrow \mathrm{\underline{coHom}}(b,c) \otimes \mathrm{\underline{coHom}}(a,b)</span>.</p>

<p><a id="X82A183B0807A0A01" name="X82A183B0807A0A01"></a></p>

<h5>1.8-21 MonoidalPreCoComposeMorphismWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ MonoidalPreCoComposeMorphismWithGivenObjects</code>( <var class="Arg">s</var>, <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">c</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( s, r )</span>.</p>

<p>The arguments are an object <span class="Math">s = \mathrm{\underline{coHom}}(a,c)</span>, three objects <span class="Math">a,b,c</span>, and an object <span class="Math">r = \mathrm{\underline{coHom}}(a,b) \otimes \mathrm{\underline{coHom}}(b,c)</span>. The output is the precocomposition morphism <span class="Math">\mathrm{MonoidalPreCoComposeMorphismWithGivenObjects}_{a,b,c}: \mathrm{\underline{coHom}}(a,c) \rightarrow \mathrm{\underline{coHom}}(b,c) \otimes \mathrm{\underline{coHom}}(a,b)</span>.</p>

<p><a id="X83FE0B8D853A76C1" name="X83FE0B8D853A76C1"></a></p>

<h5>1.8-22 MonoidalPostCoComposeMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ MonoidalPostCoComposeMorphism</code>( <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">c</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( \mathrm{\underline{coHom}}(a,c), \mathrm{\underline{coHom}}(a,b) \otimes \mathrm{\underline{coHom}}(b,c) )</span>.</p>

<p>The arguments are three objects <span class="Math">a,b,c</span>. The output is the postcocomposition morphism <span class="Math">\mathrm{MonoidalPostCoComposeMorphism}_{a,b,c}: \mathrm{\underline{coHom}}(a,c) \rightarrow \mathrm{\underline{coHom}}(a,b) \otimes \mathrm{\underline{coHom}}(b,c)</span>.</p>

<p><a id="X805DF38880B1E9E0" name="X805DF38880B1E9E0"></a></p>

<h5>1.8-23 MonoidalPostCoComposeMorphismWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ MonoidalPostCoComposeMorphismWithGivenObjects</code>( <var class="Arg">s</var>, <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">c</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( s, r )</span>.</p>

<p>The arguments are an object <span class="Math">s = \mathrm{\underline{coHom}}(a,c)</span>, three objects <span class="Math">a,b,c</span>, and an object <span class="Math">r = \mathrm{\underline{coHom}}(b,c) \otimes \mathrm{\underline{coHom}}(a,b)</span>. The output is the postcocomposition morphism <span class="Math">\mathrm{MonoidalPostCoComposeMorphismWithGivenObjects}_{a,b,c}: \mathrm{\underline{coHom}}(a,c) \rightarrow \mathrm{\underline{coHom}}(a,b) \otimes \mathrm{\underline{coHom}}(b,c)</span>.</p>

<p><a id="X817A1F7986256461" name="X817A1F7986256461"></a></p>

<h5>1.8-24 CoDualOnObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ CoDualOnObjects</code>( <var class="Arg">a</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: an object</p>

<p>The argument is an object <span class="Math">a</span>. The output is its codual object <span class="Math">a_{\vee}</span>.</p>

<p><a id="X840CBC837926138E" name="X840CBC837926138E"></a></p>

<h5>1.8-25 CoDualOnMorphisms</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ CoDualOnMorphisms</code>( <var class="Arg">alpha</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( b_{\vee}, a_{\vee} )</span>.</p>

<p>The argument is a morphism <span class="Math">\alpha: a \rightarrow b</span>. The output is its codual morphism <span class="Math">\alpha_{\vee}: b_{\vee} \rightarrow a_{\vee}</span>.</p>

<p><a id="X79750BFD824D2AAF" name="X79750BFD824D2AAF"></a></p>

<h5>1.8-26 CoDualOnMorphismsWithGivenCoDuals</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ CoDualOnMorphismsWithGivenCoDuals</code>( <var class="Arg">s</var>, <var class="Arg">alpha</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( s, r )</span>.</p>

<p>The argument is an object <span class="Math">s = b_{\vee}</span>, a morphism <span class="Math">\alpha: a \rightarrow b</span>, and an object <span class="Math">r = a_{\vee}</span>. The output is the dual morphism <span class="Math">\alpha_{\vee}: b^{\vee} \rightarrow a^{\vee}</span>.</p>

<p><a id="X7C65C05A788415E4" name="X7C65C05A788415E4"></a></p>

<h5>1.8-27 CoclosedEvaluationForCoDual</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ CoclosedEvaluationForCoDual</code>( <var class="Arg">a</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( 1, a_{\vee} \otimes a )</span>.</p>

<p>The argument is an object <span class="Math">a</span>. The output is the coclosed evaluation morphism <span class="Math">\mathrm{coclev}_{a}: 1 \rightarrow a_{\vee} \otimes a</span>.</p>

<p><a id="X7CAB615C86D97CE8" name="X7CAB615C86D97CE8"></a></p>

<h5>1.8-28 CoclosedEvaluationForCoDualWithGivenTensorProduct</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ CoclosedEvaluationForCoDualWithGivenTensorProduct</code>( <var class="Arg">s</var>, <var class="Arg">a</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( s, r )</span>.</p>

<p>The arguments are an object <span class="Math">s = 1</span>, an object <span class="Math">a</span>, and an object <span class="Math">r = a_{\vee} \otimes a</span>. The output is the coclosed evaluation morphism <span class="Math">\mathrm{coclev}_{a}: 1 \rightarrow a_{\vee} \otimes a</span>.</p>

<p><a id="X7841B6757A510799" name="X7841B6757A510799"></a></p>

<h5>1.8-29 MorphismFromCoBidual</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ MorphismFromCoBidual</code>( <var class="Arg">a</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}((a_{\vee})_{\vee}, a)</span>.</p>

<p>The argument is an object <span class="Math">a</span>. The output is the morphism from the cobidual <span class="Math">(a_{\vee})_{\vee} \rightarrow a</span>.</p>

<p><a id="X7B2B002979E1CBF6" name="X7B2B002979E1CBF6"></a></p>

<h5>1.8-30 MorphismFromCoBidualWithGivenCoBidual</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ MorphismFromCoBidualWithGivenCoBidual</code>( <var class="Arg">a</var>, <var class="Arg">s</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(s, a)</span>.</p>

<p>The arguments are an object <span class="Math">a</span>, and an object <span class="Math">s = (a_{\vee})_{\vee}</span>. The output is the morphism from the cobidual <span class="Math">(a_{\vee})_{\vee} \rightarrow a</span>.</p>

<p><a id="X7D9E57197C820E0E" name="X7D9E57197C820E0E"></a></p>

<h5>1.8-31 InternalCoHomTensorProductCompatibilityMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ InternalCoHomTensorProductCompatibilityMorphism</code>( <var class="Arg">list</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( \mathrm{\underline{coHom}}(a \otimes a', b \otimes b'), \mathrm{\underline{coHom}}(a,b) \otimes \mathrm{\underline{coHom}}(a',b'))</span>.</p>

<p>The argument is a list of four objects <span class="Math">[ a, a', b, b' ]</span>. The output is the natural morphism <span class="Math">\mathrm{InternalCoHomTensorProductCompatibilityMorphism}_{a,a',b,b'}: \mathrm{\underline{coHom}}(a \otimes a', b \otimes b') \rightarrow \mathrm{\underline{coHom}}(a,b) \otimes \mathrm{\underline{coHom}}(a',b')</span>.</p>

<p><a id="X81E9DC8D7FCD361F" name="X81E9DC8D7FCD361F"></a></p>

<h5>1.8-32 InternalCoHomTensorProductCompatibilityMorphismWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ InternalCoHomTensorProductCompatibilityMorphismWithGivenObjects</code>( <var class="Arg">s</var>, <var class="Arg">list</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( s, r )</span>.</p>

<p>The arguments are a list of four objects <span class="Math">[ a, a', b, b' ]</span>, and two objects <span class="Math">s = \mathrm{\underline{coHom}}(a \otimes a', b \otimes b')</span> and <span class="Math">r = \mathrm{\underline{coHom}}(a,b) \otimes \mathrm{\underline{coHom}}(a',b')</span>. The output is the natural morphism <span class="Math">\mathrm{InternalCoHomTensorProductCompatibilityMorphismWithGivenObjects}_{a,a',b,b'}: \mathrm{\underline{coHom}}(a \otimes a', b \otimes b') \rightarrow \mathrm{\underline{coHom}}(a,b) \otimes \mathrm{\underline{coHom}}(a',b')</span>.</p>

<p><a id="X7B817BC97C1F1DF8" name="X7B817BC97C1F1DF8"></a></p>

<h5>1.8-33 CoDualityTensorProductCompatibilityMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ CoDualityTensorProductCompatibilityMorphism</code>( <var class="Arg">a</var>, <var class="Arg">b</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( (a \otimes b)_{\vee}, a_{\vee} \otimes b_{\vee} )</span>.</p>

<p>The arguments are two objects <span class="Math">a,b</span>. The output is the natural morphism <span class="Math">\mathrm{CoDualityTensorProductCompatibilityMorphism}: (a \otimes b)_{\vee} \rightarrow a_{\vee} \otimes b_{\vee}</span>.</p>

<p><a id="X82119ED686D3874C" name="X82119ED686D3874C"></a></p>

<h5>1.8-34 CoDualityTensorProductCompatibilityMorphismWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ CoDualityTensorProductCompatibilityMorphismWithGivenObjects</code>( <var class="Arg">s</var>, <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( s, r )</span>.</p>

<p>The arguments are an object <span class="Math">s = (a \otimes b)_{\vee}</span>, two objects <span class="Math">a,b</span>, and an object <span class="Math">r = a_{\vee} \otimes b_{\vee}</span>. The output is the natural morphism <span class="Math">\mathrm{CoDualityTensorProductCompatibilityMorphismWithGivenObjects}_{a,b}: (a \otimes b)_{\vee} \rightarrow a_{\vee} \otimes b_{\vee}</span>.</p>

<p><a id="X7A4971267B80B14F" name="X7A4971267B80B14F"></a></p>

<h5>1.8-35 MorphismFromInternalCoHomToTensorProduct</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ MorphismFromInternalCoHomToTensorProduct</code>( <var class="Arg">a</var>, <var class="Arg">b</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( \mathrm{\underline{coHom}}(a,b), b_{\vee} \otimes a )</span>.</p>

<p>The arguments are two objects <span class="Math">a,b</span>. The output is the natural morphism <span class="Math">\mathrm{MorphismFromInternalCoHomToTensorProduct}_{a,b}: \mathrm{\underline{coHom}}(a,b) \rightarrow b_{\vee} \otimes a</span>.</p>

<p><a id="X7B60FB927C37E125" name="X7B60FB927C37E125"></a></p>

<h5>1.8-36 MorphismFromInternalCoHomToTensorProductWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ MorphismFromInternalCoHomToTensorProductWithGivenObjects</code>( <var class="Arg">s</var>, <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( s, r )</span>.</p>

<p>The arguments are an object <span class="Math">s = \mathrm{\underline{coHom}}(a,b)</span>, two objects <span class="Math">a,b</span>, and an object <span class="Math">r = b_{\vee} \otimes a</span>. The output is the natural morphism <span class="Math">\mathrm{MorphismFromInternalCoHomToTensorProductWithGivenObjects}_{a,b}: \mathrm{\underline{coHom}}(a,b) \rightarrow a \otimes b_{\vee}</span>.</p>

<p><a id="X86C7E40C85318EFA" name="X86C7E40C85318EFA"></a></p>

<h5>1.8-37 IsomorphismFromCoDualObjectToInternalCoHomFromTensorUnit</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsomorphismFromCoDualObjectToInternalCoHomFromTensorUnit</code>( <var class="Arg">a</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(a_{\vee}, \mathrm{\underline{coHom}}(1,a))</span>.</p>

<p>The argument is an object <span class="Math">a</span>. The output is the isomorphism <span class="Math">\mathrm{IsomorphismFromCoDualObjectToInternalCoHomFromTensorUnit}_{a}: a_{\vee} \rightarrow \mathrm{\underline{coHom}}(1,a)</span>.</p>

<p><a id="X84C86E29800BB8BC" name="X84C86E29800BB8BC"></a></p>

<h5>1.8-38 IsomorphismFromInternalCoHomFromTensorUnitToCoDualObject</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsomorphismFromInternalCoHomFromTensorUnitToCoDualObject</code>( <var class="Arg">a</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(\mathrm{\underline{coHom}}(1,a), a_{\vee})</span>.</p>

<p>The argument is an object <span class="Math">a</span>. The output is the isomorphism <span class="Math">\mathrm{IsomorphismFromInternalCoHomFromTensorUnitToCoDualObject}_{a}: \mathrm{\underline{coHom}}(1,a) \rightarrow a_{\vee}</span>.</p>

<p><a id="X7AEE412D80799D09" name="X7AEE412D80799D09"></a></p>

<h5>1.8-39 UniversalPropertyOfCoDual</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ UniversalPropertyOfCoDual</code>( <var class="Arg">t</var>, <var class="Arg">a</var>, <var class="Arg">alpha</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(a_{\vee}, t)</span>.</p>

<p>The arguments are two objects <span class="Math">t,a</span>, and a morphism <span class="Math">\alpha: 1 \rightarrow t \otimes a</span>. The output is the morphism <span class="Math">a_{\vee} \rightarrow t</span> given by the universal property of <span class="Math">a_{\vee}</span>.</p>

<p><a id="X784CBFB984E66E7A" name="X784CBFB984E66E7A"></a></p>

<h5>1.8-40 CoLambdaIntroduction</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ CoLambdaIntroduction</code>( <var class="Arg">alpha</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( \mathrm{\underline{coHom}}(a,b), 1 )</span>.</p>

<p>The argument is a morphism <span class="Math">\alpha: a \rightarrow b</span>. The output is the corresponding morphism <span class="Math"> \mathrm{\underline{coHom}}(a,b) \rightarrow 1</span> under the cohom tensor adjunction.</p>

<p><a id="X83520B098068CF62" name="X83520B098068CF62"></a></p>

<h5>1.8-41 CoLambdaElimination</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ CoLambdaElimination</code>( <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">alpha</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(a,b)</span>.</p>

<p>The arguments are two objects <span class="Math">a,b</span>, and a morphism <span class="Math">\alpha: \mathrm{\underline{coHom}}(a,b) \rightarrow 1</span>. The output is a morphism <span class="Math">a \rightarrow b</span> corresponding to <span class="Math">\alpha</span> under the cohom tensor adjunction.</p>

<p><a id="X83F11F6184DBD507" name="X83F11F6184DBD507"></a></p>

<h5>1.8-42 IsomorphismFromObjectToInternalCoHom</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsomorphismFromObjectToInternalCoHom</code>( <var class="Arg">a</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(a, \mathrm{\underline{coHom}}(a,1))</span>.</p>

<p>The argument is an object <span class="Math">a</span>. The output is the natural isomorphism <span class="Math">a \rightarrow \mathrm{\underline{coHom}}(a,1)</span>.</p>

<p><a id="X8233C995828387E9" name="X8233C995828387E9"></a></p>

<h5>1.8-43 IsomorphismFromObjectToInternalCoHomWithGivenInternalCoHom</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsomorphismFromObjectToInternalCoHomWithGivenInternalCoHom</code>( <var class="Arg">a</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(a, r)</span>.</p>

<p>The argument is an object <span class="Math">a</span>, and an object <span class="Math">r = \mathrm{\underline{coHom}}(a,1)</span>. The output is the natural isomorphism <span class="Math">a \rightarrow \mathrm{\underline{coHom}}(a,1)</span>.</p>

<p><a id="X875A349280E2095C" name="X875A349280E2095C"></a></p>

<h5>1.8-44 IsomorphismFromInternalCoHomToObject</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsomorphismFromInternalCoHomToObject</code>( <var class="Arg">a</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(\mathrm{\underline{coHom}}(a,1), a)</span>.</p>

<p>The argument is an object <span class="Math">a</span>. The output is the natural isomorphism <span class="Math">\mathrm{\underline{coHom}}(a,1) \rightarrow a</span>.</p>

<p><a id="X858AD1F986BA5BB2" name="X858AD1F986BA5BB2"></a></p>

<h5>1.8-45 IsomorphismFromInternalCoHomToObjectWithGivenInternalCoHom</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsomorphismFromInternalCoHomToObjectWithGivenInternalCoHom</code>( <var class="Arg">a</var>, <var class="Arg">s</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(s, a)</span>.</p>

<p>The argument is an object <span class="Math">a</span>, and an object <span class="Math">s = \mathrm{\underline{coHom}}(a,1)</span>. The output is the natural isomorphism <span class="Math">\mathrm{\underline{coHom}}(a,1) \rightarrow a</span>.</p>

<p><a id="X849F4CB58466EAEB" name="X849F4CB58466EAEB"></a></p>

<h4>1.9 <span class="Heading">Symmetric Closed Monoidal Categories</span></h4>

<p>A monoidal category <span class="Math">\mathbf{C}</span> which is symmetric and closed is called a <em>symmetric closed monoidal category</em>.</p>

<p>The corresponding GAP property is given by <code class="code">IsSymmetricClosedMonoidalCategory</code>.</p>

<p><a id="X86F60BCA79C63F20" name="X86F60BCA79C63F20"></a></p>

<h4>1.10 <span class="Heading">Symmetric Coclosed Monoidal Categories</span></h4>

<p>A monoidal category <span class="Math">\mathbf{C}</span> which is symmetric and coclosed is called a <em>symmetric coclosed monoidal category</em>.</p>

<p>The corresponding GAP property is given by <code class="code">IsSymmetricCoclosedMonoidalCategory</code>.</p>

<p><a id="X805AEF9784062A31" name="X805AEF9784062A31"></a></p>

<h4>1.11 <span class="Heading">Rigid Symmetric Closed Monoidal Categories</span></h4>

<p>A symmetric closed monoidal category <span class="Math">\mathbf{C}</span> satisfying</p>


<ul>
<li><p>the natural morphism</p>

</li>
</ul>
<p><span class="Math">\mathrm{\underline{Hom}_\ell}(a, a') \otimes \mathrm{\underline{Hom}_\ell}(b, b') \rightarrow \mathrm{\underline{Hom}_\ell}(a \otimes b, a' \otimes b')</span> is an isomorphism,</p>


<ul>
<li><p>the natural morphism</p>

</li>
</ul>
<p><span class="Math">a \rightarrow \mathrm{\underline{Hom}_\ell}(\mathrm{\underline{Hom}_\ell}(a, 1), 1)</span> is an isomorphism is called a <em>rigid symmetric closed monoidal category</em>.</p>

<p>If no operations involving the closed structure are installed manually, the internal hom objects will be derived as <span class="Math">\mathrm{\underline{Hom}_\ell}(a,b) \coloneqq a^\vee \otimes b</span> and, in particular, <span class="Math">\mathrm{\underline{Hom}_\ell}(a,1) \coloneqq a^\vee \otimes 1</span>.</p>

<p>The corresponding GAP property is given by <code class="code">IsRigidSymmetricClosedMonoidalCategory</code>.</p>

<p><a id="X782B629D7E7835C9" name="X782B629D7E7835C9"></a></p>

<h5>1.11-1 IsomorphismFromTensorProductWithDualObjectToInternalHom</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsomorphismFromTensorProductWithDualObjectToInternalHom</code>( <var class="Arg">a</var>, <var class="Arg">b</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( a^{\vee} \otimes b, \mathrm{\underline{Hom}}(a,b) )</span>.</p>

<p>The arguments are two objects <span class="Math">a,b</span>. The output is the natural morphism <span class="Math">\mathrm{IsomorphismFromTensorProductWithDualObjectToInternalHom}_{a,b}: a^{\vee} \otimes b \rightarrow \mathrm{\underline{Hom}}(a,b)</span>.</p>

<p><a id="X84D0668C7CA0B63D" name="X84D0668C7CA0B63D"></a></p>

<h5>1.11-2 IsomorphismFromInternalHomToTensorProductWithDualObject</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsomorphismFromInternalHomToTensorProductWithDualObject</code>( <var class="Arg">a</var>, <var class="Arg">b</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( \mathrm{\underline{Hom}}(a,b), a^{\vee} \otimes b )</span>.</p>

<p>The arguments are two objects <span class="Math">a,b</span>. The output is the inverse of <span class="Math">\mathrm{IsomorphismFromTensorProductWithDualObjectToInternalHom}</span>, namely <span class="Math">\mathrm{IsomorphismFromInternalHomToTensorProductWithDualObject}_{a,b}: \mathrm{\underline{Hom}}(a,b) \rightarrow a^{\vee} \otimes b</span>.</p>

<p><a id="X7D189B8280CECBA2" name="X7D189B8280CECBA2"></a></p>

<h5>1.11-3 MorphismFromInternalHomToTensorProduct</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ MorphismFromInternalHomToTensorProduct</code>( <var class="Arg">a</var>, <var class="Arg">b</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( \mathrm{\underline{Hom}}(a,b), a^{\vee} \otimes b )</span>.</p>

<p>The arguments are two objects <span class="Math">a,b</span>. The output is the inverse of <span class="Math">\mathrm{MorphismFromTensorProductToInternalHomWithGivenObjects}</span>, namely <span class="Math">\mathrm{MorphismFromInternalHomToTensorProductWithGivenObjects}_{a,b}: \mathrm{\underline{Hom}}(a,b) \rightarrow a^{\vee} \otimes b</span>.</p>

<p><a id="X7D10805D840AAC8D" name="X7D10805D840AAC8D"></a></p>

<h5>1.11-4 MorphismFromInternalHomToTensorProductWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ MorphismFromInternalHomToTensorProductWithGivenObjects</code>( <var class="Arg">s</var>, <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( \mathrm{\underline{Hom}}(a,b), a^{\vee} \otimes b )</span>.</p>

<p>The arguments are an object <span class="Math">s = \mathrm{\underline{Hom}}(a,b)</span>, two objects <span class="Math">a,b</span>, and an object <span class="Math">r = a^{\vee} \otimes b</span>. The output is the inverse of <span class="Math">\mathrm{MorphismFromTensorProductToInternalHomWithGivenObjects}</span>, namely <span class="Math">\mathrm{MorphismFromInternalHomToTensorProductWithGivenObjects}_{a,b}: \mathrm{\underline{Hom}}(a,b) \rightarrow a^{\vee} \otimes b</span>.</p>

<p><a id="X85BA8C10817296F7" name="X85BA8C10817296F7"></a></p>

<h5>1.11-5 TensorProductInternalHomCompatibilityMorphismInverse</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TensorProductInternalHomCompatibilityMorphismInverse</code>( <var class="Arg">list</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( \mathrm{\underline{Hom}}(a \otimes b,a' \otimes b'), \mathrm{\underline{Hom}}(a,a') \otimes \mathrm{\underline{Hom}}(b,b') )</span>.</p>

<p>The argument is a list of four objects <span class="Math">[ a, a', b, b' ]</span>. The output is the natural morphism <span class="Math">\mathrm{TensorProductInternalHomCompatibilityMorphismInverseWithGivenObjects}_{a,a',b,b'}: \mathrm{\underline{Hom}}(a \otimes b,a' \otimes b') \rightarrow \mathrm{\underline{Hom}}(a,a') \otimes \mathrm{\underline{Hom}}(b,b')</span>.</p>

<p><a id="X7CCE67B281EF45C1" name="X7CCE67B281EF45C1"></a></p>

<h5>1.11-6 TensorProductInternalHomCompatibilityMorphismInverseWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TensorProductInternalHomCompatibilityMorphismInverseWithGivenObjects</code>( <var class="Arg">s</var>, <var class="Arg">list</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( \mathrm{\underline{Hom}}(a \otimes b,a' \otimes b'), \mathrm{\underline{Hom}}(a,a') \otimes \mathrm{\underline{Hom}}(b,b') )</span>.</p>

<p>The arguments are a list of four objects <span class="Math">[ a, a', b, b' ]</span>, and two objects <span class="Math">s = \mathrm{\underline{Hom}}(a \otimes b,a' \otimes b')</span> and <span class="Math">r = \mathrm{\underline{Hom}}(a,a') \otimes \mathrm{\underline{Hom}}(b,b')</span>. The output is the natural morphism <span class="Math">\mathrm{TensorProductInternalHomCompatibilityMorphismInverseWithGivenObjects}_{a,a',b,b'}: \mathrm{\underline{Hom}}(a \otimes b,a' \otimes b') \rightarrow \mathrm{\underline{Hom}}(a,a') \otimes \mathrm{\underline{Hom}}(b,b')</span>.</p>

<p><a id="X83849B327C8074E9" name="X83849B327C8074E9"></a></p>

<h5>1.11-7 CoevaluationForDual</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ CoevaluationForDual</code>( <var class="Arg">a</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(1,a \otimes a^{\vee})</span>.</p>

<p>The argument is an object <span class="Math">a</span>. The output is the coevaluation morphism <span class="Math">\mathrm{coev}_{a}:1 \rightarrow a \otimes a^{\vee}</span>.</p>

<p><a id="X7C65E6A97AAE0DE3" name="X7C65E6A97AAE0DE3"></a></p>

<h5>1.11-8 CoevaluationForDualWithGivenTensorProduct</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ CoevaluationForDualWithGivenTensorProduct</code>( <var class="Arg">s</var>, <var class="Arg">a</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(1,a \otimes a^{\vee})</span>.</p>

<p>The arguments are an object <span class="Math">s = 1</span>, an object <span class="Math">a</span>, and an object <span class="Math">r = a \otimes a^{\vee}</span>. The output is the coevaluation morphism <span class="Math">\mathrm{coev}_{a}:1 \rightarrow a \otimes a^{\vee}</span>.</p>

<p><a id="X85D0C9487A22AFFE" name="X85D0C9487A22AFFE"></a></p>

<h5>1.11-9 TraceMap</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TraceMap</code>( <var class="Arg">alpha</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(1,1)</span>.</p>

<p>The argument is an endomorphism <span class="Math">\alpha: a \rightarrow a</span>. The output is the trace morphism <span class="Math">\mathrm{trace}_{\alpha}: 1 \rightarrow 1</span>.</p>

<p><a id="X82F0DBD485D93793" name="X82F0DBD485D93793"></a></p>

<h5>1.11-10 RankMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ RankMorphism</code>( <var class="Arg">a</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(1,1)</span>.</p>

<p>The argument is an object <span class="Math">a</span>. The output is the rank morphism <span class="Math">\mathrm{rank}_a: 1 \rightarrow 1</span>.</p>

<p><a id="X7E02E8197EA201EA" name="X7E02E8197EA201EA"></a></p>

<h5>1.11-11 MorphismFromBidual</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ MorphismFromBidual</code>( <var class="Arg">a</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}((a^{\vee})^{\vee},a)</span>.</p>

<p>The argument is an object <span class="Math">a</span>. The output is the inverse of the morphism to the bidual <span class="Math">(a^{\vee})^{\vee} \rightarrow a</span>.</p>

<p><a id="X785CF0BB7BC0AC0D" name="X785CF0BB7BC0AC0D"></a></p>

<h5>1.11-12 MorphismFromBidualWithGivenBidual</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ MorphismFromBidualWithGivenBidual</code>( <var class="Arg">a</var>, <var class="Arg">s</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}((a^{\vee})^{\vee},a)</span>.</p>

<p>The argument is an object <span class="Math">a</span>, and an object <span class="Math">s = (a^{\vee})^{\vee}</span>. The output is the inverse of the morphism to the bidual <span class="Math">(a^{\vee})^{\vee} \rightarrow a</span>.</p>

<p><a id="X79E86CAD853AB883" name="X79E86CAD853AB883"></a></p>

<h4>1.12 <span class="Heading">Rigid Symmetric Coclosed Monoidal Categories</span></h4>

<p>A symmetric coclosed monoidal category <span class="Math">\mathbf{C}</span> satisfying</p>


<ul>
<li><p>the natural morphism</p>

</li>
</ul>
<p><span class="Math">\mathrm{\underline{coHom}}(a \otimes a', b \otimes b') \rightarrow \mathrm{\underline{coHom}}(a, b) \otimes \mathrm{\underline{coHom}}(a', b')</span> is an isomorphism,</p>


<ul>
<li><p>the natural morphism</p>

</li>
</ul>
<p><span class="Math">\mathrm{\underline{coHom}}(1, \mathrm{\underline{coHom}}(1, a)) \rightarrow a</span> is an isomorphism is called a <em>rigid symmetric coclosed monoidal category</em>.</p>

<p>If no operations involving the coclosed structure are installed manually, the internal cohom objects will be derived as <span class="Math">\mathrm{\underline{coHom}}(a,b) \coloneqq a \otimes b_\vee</span> and, in particular, <span class="Math">\mathrm{\underline{coHom}}(1,a) \coloneqq 1 \otimes a_\vee</span>.</p>

<p>The corresponding GAP property is given by <code class="code">IsRigidSymmetricCoclosedMonoidalCategory</code>.</p>

<p><a id="X82D4EF587F1C194C" name="X82D4EF587F1C194C"></a></p>

<h5>1.12-1 IsomorphismFromInternalCoHomToTensorProductWithCoDualObject</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsomorphismFromInternalCoHomToTensorProductWithCoDualObject</code>( <var class="Arg">a</var>, <var class="Arg">b</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( \mathrm{\underline{coHom}}(a,b), b_{\vee} \otimes a )</span>.</p>

<p>The arguments are two objects <span class="Math">a,b</span>. The output is the natural morphism <span class="Math">\mathrm{IsomorphismFromInternalCoHomToTensorProductWithCoDualObjectWithGivenObjects}_{a,b}: \mathrm{\underline{coHom}}(a,b) \rightarrow b_{\vee} \otimes a</span>.</p>

<p><a id="X7FE736BA834D228A" name="X7FE736BA834D228A"></a></p>

<h5>1.12-2 IsomorphismFromTensorProductWithCoDualObjectToInternalCoHom</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsomorphismFromTensorProductWithCoDualObjectToInternalCoHom</code>( <var class="Arg">a</var>, <var class="Arg">b</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( a_{\vee} \otimes b, \mathrm{\underline{coHom}}(b,a)</span>.</p>

<p>The arguments are two objects <span class="Math">a,b</span>. The output is the inverse of <span class="Math">\mathrm{IsomorphismFromInternalCoHomToTensorProductWithCoDualObject}</span>, namely <span class="Math">\mathrm{IsomorphismFromTensorProductWithCoDualObjectToInternalCoHom}_{a,b}: a_{\vee} \otimes b \rightarrow \mathrm{\underline{coHom}}(b,a)</span>.</p>

<p><a id="X7DCA54857A6B45DF" name="X7DCA54857A6B45DF"></a></p>

<h5>1.12-3 MorphismFromTensorProductToInternalCoHom</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ MorphismFromTensorProductToInternalCoHom</code>( <var class="Arg">a</var>, <var class="Arg">b</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( a_{\vee} \otimes b, \mathrm{\underline{coHom}}(b,a) )</span>.</p>

<p>The arguments are two objects <span class="Math">a,b</span>. The output is the inverse of <span class="Math">\mathrm{MorphismFromInternalCoHomToTensorProductWithGivenObjects}</span>, namely <span class="Math">\mathrm{MorphismFromTensorProductToInternalCoHomWithGivenObjects}_{a,b}: a_{\vee} \otimes b \rightarrow \mathrm{\underline{coHom}}(b,a)</span>.</p>

<p><a id="X7888F9947DDC15B5" name="X7888F9947DDC15B5"></a></p>

<h5>1.12-4 MorphismFromTensorProductToInternalCoHomWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ MorphismFromTensorProductToInternalCoHomWithGivenObjects</code>( <var class="Arg">s</var>, <var class="Arg">a</var>, <var class="Arg">b</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( a_{\vee} \otimes b, \mathrm{\underline{coHom}}(b,a)</span>.</p>

<p>The arguments are an object <span class="Math">s_{\vee} = a \otimes b</span>, two objects <span class="Math">a,b</span>, and an object <span class="Math">r = \mathrm{\underline{coHom}}(b,a)</span>. The output is the inverse of <span class="Math">\mathrm{MorphismFromInternalCoHomToTensorProductWithGivenObjects}</span>, namely <span class="Math">\mathrm{MorphismFromTensorProductToInternalCoHomWithGivenObjects}_{a,b}: a_{\vee} \otimes b \rightarrow \mathrm{\underline{coHom}}(b,a)</span>.</p>

<p><a id="X7E71AF0985C5AEC5" name="X7E71AF0985C5AEC5"></a></p>

<h5>1.12-5 InternalCoHomTensorProductCompatibilityMorphismInverse</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ InternalCoHomTensorProductCompatibilityMorphismInverse</code>( <var class="Arg">list</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( \mathrm{\underline{coHom}}(a,b) \otimes \mathrm{\underline{coHom}}(a',b'), \mathrm{\underline{coHom}}(a \otimes a', b \otimes b' )</span>.</p>

<p>The argument is a list of four objects <span class="Math">[ a, a', b, b' ]</span>. The output is the natural morphism <span class="Math">\mathrm{InternalCoHomTensorProductCompatibilityMorphismInverseWithGivenObjects}_{a,a',b,b'}: \mathrm{\underline{coHom}}(a,b) \otimes \mathrm{\underline{coHom}}(a',b') \rightarrow \mathrm{\underline{coHom}}(a \otimes a', b \otimes b')</span>.</p>

<p><a id="X87BF8BE67AD5ABCF" name="X87BF8BE67AD5ABCF"></a></p>

<h5>1.12-6 InternalCoHomTensorProductCompatibilityMorphismInverseWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ InternalCoHomTensorProductCompatibilityMorphismInverseWithGivenObjects</code>( <var class="Arg">s</var>, <var class="Arg">list</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}( \mathrm{\underline{coHom}}(a,b) \otimes \mathrm{\underline{coHom}}(a',b'), \mathrm{\underline{coHom}}(a \otimes a', b \otimes b' )</span>.</p>

<p>The arguments are a list of four objects <span class="Math">[ a, a', b, b' ]</span>, and two objects <span class="Math">s = \mathrm{\underline{coHom}}(a,b) \otimes \mathrm{\underline{coHom}}(a',b')</span> and <span class="Math">r = \mathrm{\underline{coHom}}(a \otimes a', b \otimes b')</span>. The output is the natural morphism <span class="Math">\mathrm{InternalCoHomTensorProductCompatibilityMorphismInverseWithGivenObjects}_{a,a',b,b'}: \mathrm{\underline{coHom}}(a,b) \otimes \mathrm{\underline{coHom}}(a',b') \rightarrow \mathrm{\underline{coHom}}(a \otimes a', b \otimes b')</span>.</p>

<p><a id="X8695F9D97A8C6C61" name="X8695F9D97A8C6C61"></a></p>

<h5>1.12-7 CoclosedCoevaluationForCoDual</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ CoclosedCoevaluationForCoDual</code>( <var class="Arg">a</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(a \otimes a_{\vee}, 1)</span>.</p>

<p>The argument is an object <span class="Math">a</span>. The output is the coclosed coevaluation morphism <span class="Math">\mathrm{coclcoev}_{a}: a \otimes a_{\vee} \rightarrow 1</span>.</p>

<p><a id="X78B2703A7B81E340" name="X78B2703A7B81E340"></a></p>

<h5>1.12-8 CoclosedCoevaluationForCoDualWithGivenTensorProduct</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ CoclosedCoevaluationForCoDualWithGivenTensorProduct</code>( <var class="Arg">s</var>, <var class="Arg">a</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(a \otimes a_{\vee}, 1)</span>.</p>

<p>The arguments are an object <span class="Math">s = a \otimes a_{\vee}</span>, an object <span class="Math">a</span>, and an object <span class="Math">r = 1</span>. The output is the coclosed coevaluation morphism <span class="Math">\mathrm{coclcoev}_{a}: a \otimes a_{\vee} \rightarrow 1</span>.</p>

<p><a id="X829BE5F97A656200" name="X829BE5F97A656200"></a></p>

<h5>1.12-9 CoTraceMap</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ CoTraceMap</code>( <var class="Arg">alpha</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(1,1)</span>.</p>

<p>The argument is an endomorphism <span class="Math">\alpha: a \rightarrow a</span>. The output is the cotrace morphism <span class="Math">\mathrm{cotrace}_{\alpha}: 1 \rightarrow 1</span>.</p>

<p><a id="X7C5CC8F97D95AD43" name="X7C5CC8F97D95AD43"></a></p>

<h5>1.12-10 CoRankMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ CoRankMorphism</code>( <var class="Arg">a</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(1,1)</span>.</p>

<p>The argument is an object <span class="Math">a</span>. The output is the corank morphism <span class="Math">\mathrm{corank}_a: 1 \rightarrow 1</span>.</p>

<p><a id="X85BDB94D85C67725" name="X85BDB94D85C67725"></a></p>

<h5>1.12-11 MorphismToCoBidual</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ MorphismToCoBidual</code>( <var class="Arg">a</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(a, (a_{\vee})_{\vee})</span>.</p>

<p>The argument is an object <span class="Math">a</span>. The output is the inverse of the morphism from the cobidual <span class="Math">a \rightarrow (a_{\vee})_{\vee}</span>.</p>

<p><a id="X800035BF867418D0" name="X800035BF867418D0"></a></p>

<h5>1.12-12 MorphismToCoBidualWithGivenCoBidual</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ MorphismToCoBidualWithGivenCoBidual</code>( <var class="Arg">a</var>, <var class="Arg">r</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism in <span class="Math">\mathrm{Hom}(a,(a_{\vee})_{\vee})</span>.</p>

<p>The argument is an object <span class="Math">a</span>, and an object <span class="Math">r = (a_{\vee})_{\vee}</span>. The output is the inverse of the morphism from the cobidual <span class="Math">a \rightarrow (a_{\vee})_{\vee}</span>.</p>

<p><a id="X7B40ED8B78D067A5" name="X7B40ED8B78D067A5"></a></p>

<h4>1.13 <span class="Heading">Convenience Methods</span></h4>

<p><a id="X8055FF847AC2102A" name="X8055FF847AC2102A"></a></p>

<h5>1.13-1 InternalHom</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ InternalHom</code>( <var class="Arg">a</var>, <var class="Arg">b</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a cell</p>

<p>This is a convenience method. The arguments are two cells <span class="Math">a,b</span>. The output is the internal hom cell. If <span class="Math">a,b</span> are two CAP objects the output is the internal Hom object <span class="Math">\mathrm{\underline{Hom}}(a,b)</span>. If at least one of the arguments is a CAP morphism the output is a CAP morphism, namely the internal hom on morphisms, where any object is replaced by its identity morphism.</p>

<p><a id="X7CB6A9497A971F59" name="X7CB6A9497A971F59"></a></p>

<h5>1.13-2 InternalCoHom</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ InternalCoHom</code>( <var class="Arg">a</var>, <var class="Arg">b</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a cell</p>

<p>This is a convenience method. The arguments are two cells <span class="Math">a,b</span>. The output is the internal cohom cell. If <span class="Math">a,b</span> are two CAP objects the output is the internal cohom object <span class="Math">\mathrm{\underline{coHom}}(a,b)</span>. If at least one of the arguments is a CAP morphism the output is a CAP morphism, namely the internal cohom on morphisms, where any object is replaced by its identity morphism.</p>

<p><a id="X82DE5FDA794914A0" name="X82DE5FDA794914A0"></a></p>

<h5>1.13-3 LeftInternalHom</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftInternalHom</code>( <var class="Arg">a</var>, <var class="Arg">b</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a cell</p>

<p>This is a convenience method. The arguments are two cells <span class="Math">a,b</span>. The output is the internal hom cell. If <span class="Math">a,b</span> are two CAP objects the output is the internal Hom object <span class="Math">\mathrm{\underline{Hom}_\ell}(a,b)</span>. If at least one of the arguments is a CAP morphism the output is a CAP morphism, namely the internal hom on morphisms, where any object is replaced by its identity morphism.</p>

<p><a id="X862E6A787C9E1F92" name="X862E6A787C9E1F92"></a></p>

<h5>1.13-4 LeftInternalCoHom</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LeftInternalCoHom</code>( <var class="Arg">a</var>, <var class="Arg">b</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a cell</p>

<p>This is a convenience method. The arguments are two cells <span class="Math">a,b</span>. The output is the internal cohom cell. If <span class="Math">a,b</span> are two CAP objects the output is the internal cohom object <span class="Math">\mathrm{\underline{coHom}_\ell}(a,b)</span>. If at least one of the arguments is a CAP morphism the output is a CAP morphism, namely the internal cohom on morphisms, where any object is replaced by its identity morphism.</p>

<p><a id="X85C8C80F785AEB5E" name="X85C8C80F785AEB5E"></a></p>

<h4>1.14 <span class="Heading">Add-methods</span></h4>

<p><a id="X78DA7EC37A1E0CCC" name="X78DA7EC37A1E0CCC"></a></p>

<h5>1.14-1 AddLeftDistributivityExpanding</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftDistributivityExpanding</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftDistributivityExpanding</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LeftDistributivityExpanding</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, L ) \mapsto \mathtt{LeftDistributivityExpanding}(a, L)</span>.</p>

<p><a id="X814BA200802D26E4" name="X814BA200802D26E4"></a></p>

<h5>1.14-2 AddLeftDistributivityExpandingWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftDistributivityExpandingWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftDistributivityExpandingWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LeftDistributivityExpandingWithGivenObjects</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( s, a, L, r ) \mapsto \mathtt{LeftDistributivityExpandingWithGivenObjects}(s, a, L, r)</span>.</p>

<p><a id="X8381C23A8264435B" name="X8381C23A8264435B"></a></p>

<h5>1.14-3 AddLeftDistributivityFactoring</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftDistributivityFactoring</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftDistributivityFactoring</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LeftDistributivityFactoring</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, L ) \mapsto \mathtt{LeftDistributivityFactoring}(a, L)</span>.</p>

<p><a id="X7F0A439478576973" name="X7F0A439478576973"></a></p>

<h5>1.14-4 AddLeftDistributivityFactoringWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftDistributivityFactoringWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftDistributivityFactoringWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LeftDistributivityFactoringWithGivenObjects</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( s, a, L, r ) \mapsto \mathtt{LeftDistributivityFactoringWithGivenObjects}(s, a, L, r)</span>.</p>

<p><a id="X82E93F8E79CB7338" name="X82E93F8E79CB7338"></a></p>

<h5>1.14-5 AddRightDistributivityExpanding</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddRightDistributivityExpanding</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddRightDistributivityExpanding</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">RightDistributivityExpanding</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( L, a ) \mapsto \mathtt{RightDistributivityExpanding}(L, a)</span>.</p>

<p><a id="X7A6178C17EFC817A" name="X7A6178C17EFC817A"></a></p>

<h5>1.14-6 AddRightDistributivityExpandingWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddRightDistributivityExpandingWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddRightDistributivityExpandingWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">RightDistributivityExpandingWithGivenObjects</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( s, L, a, r ) \mapsto \mathtt{RightDistributivityExpandingWithGivenObjects}(s, L, a, r)</span>.</p>

<p><a id="X79B283777BC5F12C" name="X79B283777BC5F12C"></a></p>

<h5>1.14-7 AddRightDistributivityFactoring</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddRightDistributivityFactoring</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddRightDistributivityFactoring</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">RightDistributivityFactoring</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( L, a ) \mapsto \mathtt{RightDistributivityFactoring}(L, a)</span>.</p>

<p><a id="X842099557CF2036E" name="X842099557CF2036E"></a></p>

<h5>1.14-8 AddRightDistributivityFactoringWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddRightDistributivityFactoringWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddRightDistributivityFactoringWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">RightDistributivityFactoringWithGivenObjects</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( s, L, a, r ) \mapsto \mathtt{RightDistributivityFactoringWithGivenObjects}(s, L, a, r)</span>.</p>

<p><a id="X7F9C3FD38397D9D4" name="X7F9C3FD38397D9D4"></a></p>

<h5>1.14-9 AddBraiding</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddBraiding</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddBraiding</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">Braiding</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b ) \mapsto \mathtt{Braiding}(a, b)</span>.</p>

<p><a id="X8423AA1A862E9780" name="X8423AA1A862E9780"></a></p>

<h5>1.14-10 AddBraidingInverse</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddBraidingInverse</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddBraidingInverse</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">BraidingInverse</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b ) \mapsto \mathtt{BraidingInverse}(a, b)</span>.</p>

<p><a id="X85C7E40583A5955F" name="X85C7E40583A5955F"></a></p>

<h5>1.14-11 AddBraidingInverseWithGivenTensorProducts</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddBraidingInverseWithGivenTensorProducts</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddBraidingInverseWithGivenTensorProducts</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">BraidingInverseWithGivenTensorProducts</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( s, a, b, r ) \mapsto \mathtt{BraidingInverseWithGivenTensorProducts}(s, a, b, r)</span>.</p>

<p><a id="X7A52CBE8801D6B28" name="X7A52CBE8801D6B28"></a></p>

<h5>1.14-12 AddBraidingWithGivenTensorProducts</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddBraidingWithGivenTensorProducts</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddBraidingWithGivenTensorProducts</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">BraidingWithGivenTensorProducts</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( s, a, b, r ) \mapsto \mathtt{BraidingWithGivenTensorProducts}(s, a, b, r)</span>.</p>

<p><a id="X7996A3A980BD5783" name="X7996A3A980BD5783"></a></p>

<h5>1.14-13 AddClosedMonoidalLeftCoevaluationMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddClosedMonoidalLeftCoevaluationMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddClosedMonoidalLeftCoevaluationMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">ClosedMonoidalLeftCoevaluationMorphism</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b ) \mapsto \mathtt{ClosedMonoidalLeftCoevaluationMorphism}(a, b)</span>.</p>

<p><a id="X7FD9DC1D870FB3D2" name="X7FD9DC1D870FB3D2"></a></p>

<h5>1.14-14 AddClosedMonoidalLeftCoevaluationMorphismWithGivenRange</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddClosedMonoidalLeftCoevaluationMorphismWithGivenRange</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddClosedMonoidalLeftCoevaluationMorphismWithGivenRange</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">ClosedMonoidalLeftCoevaluationMorphismWithGivenRange</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b, r ) \mapsto \mathtt{ClosedMonoidalLeftCoevaluationMorphismWithGivenRange}(a, b, r)</span>.</p>

<p><a id="X82E0E46E7B374DA9" name="X82E0E46E7B374DA9"></a></p>

<h5>1.14-15 AddClosedMonoidalLeftEvaluationMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddClosedMonoidalLeftEvaluationMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddClosedMonoidalLeftEvaluationMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">ClosedMonoidalLeftEvaluationMorphism</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b ) \mapsto \mathtt{ClosedMonoidalLeftEvaluationMorphism}(a, b)</span>.</p>

<p><a id="X8742C27B7D30E543" name="X8742C27B7D30E543"></a></p>

<h5>1.14-16 AddClosedMonoidalLeftEvaluationMorphismWithGivenSource</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddClosedMonoidalLeftEvaluationMorphismWithGivenSource</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddClosedMonoidalLeftEvaluationMorphismWithGivenSource</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">ClosedMonoidalLeftEvaluationMorphismWithGivenSource</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b, s ) \mapsto \mathtt{ClosedMonoidalLeftEvaluationMorphismWithGivenSource}(a, b, s)</span>.</p>

<p><a id="X870332B286200F2A" name="X870332B286200F2A"></a></p>

<h5>1.14-17 AddClosedMonoidalRightCoevaluationMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddClosedMonoidalRightCoevaluationMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddClosedMonoidalRightCoevaluationMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">ClosedMonoidalRightCoevaluationMorphism</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b ) \mapsto \mathtt{ClosedMonoidalRightCoevaluationMorphism}(a, b)</span>.</p>

<p><a id="X7A06D2CC79874E18" name="X7A06D2CC79874E18"></a></p>

<h5>1.14-18 AddClosedMonoidalRightCoevaluationMorphismWithGivenRange</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddClosedMonoidalRightCoevaluationMorphismWithGivenRange</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddClosedMonoidalRightCoevaluationMorphismWithGivenRange</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">ClosedMonoidalRightCoevaluationMorphismWithGivenRange</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b, r ) \mapsto \mathtt{ClosedMonoidalRightCoevaluationMorphismWithGivenRange}(a, b, r)</span>.</p>

<p><a id="X82FD88E87B30334F" name="X82FD88E87B30334F"></a></p>

<h5>1.14-19 AddClosedMonoidalRightEvaluationMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddClosedMonoidalRightEvaluationMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddClosedMonoidalRightEvaluationMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">ClosedMonoidalRightEvaluationMorphism</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b ) \mapsto \mathtt{ClosedMonoidalRightEvaluationMorphism}(a, b)</span>.</p>

<p><a id="X7ECDA3E47F267341" name="X7ECDA3E47F267341"></a></p>

<h5>1.14-20 AddClosedMonoidalRightEvaluationMorphismWithGivenSource</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddClosedMonoidalRightEvaluationMorphismWithGivenSource</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddClosedMonoidalRightEvaluationMorphismWithGivenSource</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">ClosedMonoidalRightEvaluationMorphismWithGivenSource</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b, s ) \mapsto \mathtt{ClosedMonoidalRightEvaluationMorphismWithGivenSource}(a, b, s)</span>.</p>

<p><a id="X800DFCF37CC10CCC" name="X800DFCF37CC10CCC"></a></p>

<h5>1.14-21 AddDualOnMorphisms</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddDualOnMorphisms</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddDualOnMorphisms</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">DualOnMorphisms</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( alpha ) \mapsto \mathtt{DualOnMorphisms}(alpha)</span>.</p>

<p><a id="X85DA12C581E673DE" name="X85DA12C581E673DE"></a></p>

<h5>1.14-22 AddDualOnMorphismsWithGivenDuals</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddDualOnMorphismsWithGivenDuals</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddDualOnMorphismsWithGivenDuals</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">DualOnMorphismsWithGivenDuals</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( s, alpha, r ) \mapsto \mathtt{DualOnMorphismsWithGivenDuals}(s, alpha, r)</span>.</p>

<p><a id="X7BB4DD5381EBF082" name="X7BB4DD5381EBF082"></a></p>

<h5>1.14-23 AddDualOnObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddDualOnObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddDualOnObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">DualOnObjects</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a ) \mapsto \mathtt{DualOnObjects}(a)</span>.</p>

<p><a id="X7FF9C96186646B7C" name="X7FF9C96186646B7C"></a></p>

<h5>1.14-24 AddEvaluationForDual</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddEvaluationForDual</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddEvaluationForDual</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">EvaluationForDual</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a ) \mapsto \mathtt{EvaluationForDual}(a)</span>.</p>

<p><a id="X7CB63A4E7E905CD4" name="X7CB63A4E7E905CD4"></a></p>

<h5>1.14-25 AddEvaluationForDualWithGivenTensorProduct</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddEvaluationForDualWithGivenTensorProduct</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddEvaluationForDualWithGivenTensorProduct</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">EvaluationForDualWithGivenTensorProduct</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( s, a, r ) \mapsto \mathtt{EvaluationForDualWithGivenTensorProduct}(s, a, r)</span>.</p>

<p><a id="X79A5E1EF7F091948" name="X79A5E1EF7F091948"></a></p>

<h5>1.14-26 AddInternalHomOnMorphisms</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddInternalHomOnMorphisms</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddInternalHomOnMorphisms</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">InternalHomOnMorphisms</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( alpha, beta ) \mapsto \mathtt{InternalHomOnMorphisms}(alpha, beta)</span>.</p>

<p><a id="X8070203E80388349" name="X8070203E80388349"></a></p>

<h5>1.14-27 AddInternalHomOnMorphismsWithGivenInternalHoms</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddInternalHomOnMorphismsWithGivenInternalHoms</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddInternalHomOnMorphismsWithGivenInternalHoms</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">InternalHomOnMorphismsWithGivenInternalHoms</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( s, alpha, beta, r ) \mapsto \mathtt{InternalHomOnMorphismsWithGivenInternalHoms}(s, alpha, beta, r)</span>.</p>

<p><a id="X7B74F8FD8348D590" name="X7B74F8FD8348D590"></a></p>

<h5>1.14-28 AddInternalHomOnObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddInternalHomOnObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddInternalHomOnObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">InternalHomOnObjects</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b ) \mapsto \mathtt{InternalHomOnObjects}(a, b)</span>.</p>

<p><a id="X87D40CEF8247DF33" name="X87D40CEF8247DF33"></a></p>

<h5>1.14-29 AddInternalHomToTensorProductLeftAdjunctMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddInternalHomToTensorProductLeftAdjunctMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddInternalHomToTensorProductLeftAdjunctMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">InternalHomToTensorProductLeftAdjunctMorphism</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( b, c, g ) \mapsto \mathtt{InternalHomToTensorProductLeftAdjunctMorphism}(b, c, g)</span>.</p>

<p><a id="X82D3E7BD7DD67116" name="X82D3E7BD7DD67116"></a></p>

<h5>1.14-30 AddInternalHomToTensorProductLeftAdjunctMorphismWithGivenTensorProduct</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddInternalHomToTensorProductLeftAdjunctMorphismWithGivenTensorProduct</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddInternalHomToTensorProductLeftAdjunctMorphismWithGivenTensorProduct</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">InternalHomToTensorProductLeftAdjunctMorphismWithGivenTensorProduct</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( b, c, g, s ) \mapsto \mathtt{InternalHomToTensorProductLeftAdjunctMorphismWithGivenTensorProduct}(b, c, g, s)</span>.</p>

<p><a id="X7BBC91088476613F" name="X7BBC91088476613F"></a></p>

<h5>1.14-31 AddInternalHomToTensorProductLeftAdjunctionIsomorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddInternalHomToTensorProductLeftAdjunctionIsomorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddInternalHomToTensorProductLeftAdjunctionIsomorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">InternalHomToTensorProductLeftAdjunctionIsomorphism</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b, c ) \mapsto \mathtt{InternalHomToTensorProductLeftAdjunctionIsomorphism}(a, b, c)</span>.</p>

<p><a id="X789D0ED680E7D176" name="X789D0ED680E7D176"></a></p>

<h5>1.14-32 AddInternalHomToTensorProductLeftAdjunctionIsomorphismWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddInternalHomToTensorProductLeftAdjunctionIsomorphismWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddInternalHomToTensorProductLeftAdjunctionIsomorphismWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">InternalHomToTensorProductLeftAdjunctionIsomorphismWithGivenObjects</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( s, a, b, c, r ) \mapsto \mathtt{InternalHomToTensorProductLeftAdjunctionIsomorphismWithGivenObjects}(s, a, b, c, r)</span>.</p>

<p><a id="X84B3BDBF8294E790" name="X84B3BDBF8294E790"></a></p>

<h5>1.14-33 AddInternalHomToTensorProductRightAdjunctMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddInternalHomToTensorProductRightAdjunctMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddInternalHomToTensorProductRightAdjunctMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">InternalHomToTensorProductRightAdjunctMorphism</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, c, g ) \mapsto \mathtt{InternalHomToTensorProductRightAdjunctMorphism}(a, c, g)</span>.</p>

<p><a id="X807104E57D50EEB9" name="X807104E57D50EEB9"></a></p>

<h5>1.14-34 AddInternalHomToTensorProductRightAdjunctMorphismWithGivenTensorProduct</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddInternalHomToTensorProductRightAdjunctMorphismWithGivenTensorProduct</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddInternalHomToTensorProductRightAdjunctMorphismWithGivenTensorProduct</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">InternalHomToTensorProductRightAdjunctMorphismWithGivenTensorProduct</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, c, g, s ) \mapsto \mathtt{InternalHomToTensorProductRightAdjunctMorphismWithGivenTensorProduct}(a, c, g, s)</span>.</p>

<p><a id="X8634234A855F18D5" name="X8634234A855F18D5"></a></p>

<h5>1.14-35 AddInternalHomToTensorProductRightAdjunctionIsomorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddInternalHomToTensorProductRightAdjunctionIsomorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddInternalHomToTensorProductRightAdjunctionIsomorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">InternalHomToTensorProductRightAdjunctionIsomorphism</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b, c ) \mapsto \mathtt{InternalHomToTensorProductRightAdjunctionIsomorphism}(a, b, c)</span>.</p>

<p><a id="X7A3FED8E84CD4A02" name="X7A3FED8E84CD4A02"></a></p>

<h5>1.14-36 AddInternalHomToTensorProductRightAdjunctionIsomorphismWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddInternalHomToTensorProductRightAdjunctionIsomorphismWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddInternalHomToTensorProductRightAdjunctionIsomorphismWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">InternalHomToTensorProductRightAdjunctionIsomorphismWithGivenObjects</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( s, a, b, c, r ) \mapsto \mathtt{InternalHomToTensorProductRightAdjunctionIsomorphismWithGivenObjects}(s, a, b, c, r)</span>.</p>

<p><a id="X7983CB57783E6813" name="X7983CB57783E6813"></a></p>

<h5>1.14-37 AddIsomorphismFromDualObjectToInternalHomIntoTensorUnit</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddIsomorphismFromDualObjectToInternalHomIntoTensorUnit</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddIsomorphismFromDualObjectToInternalHomIntoTensorUnit</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">IsomorphismFromDualObjectToInternalHomIntoTensorUnit</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a ) \mapsto \mathtt{IsomorphismFromDualObjectToInternalHomIntoTensorUnit}(a)</span>.</p>

<p><a id="X84E4949886CB84C9" name="X84E4949886CB84C9"></a></p>

<h5>1.14-38 AddIsomorphismFromInternalHomIntoTensorUnitToDualObject</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddIsomorphismFromInternalHomIntoTensorUnitToDualObject</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddIsomorphismFromInternalHomIntoTensorUnitToDualObject</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">IsomorphismFromInternalHomIntoTensorUnitToDualObject</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a ) \mapsto \mathtt{IsomorphismFromInternalHomIntoTensorUnitToDualObject}(a)</span>.</p>

<p><a id="X7FA9FE2B85CE866D" name="X7FA9FE2B85CE866D"></a></p>

<h5>1.14-39 AddIsomorphismFromInternalHomToObject</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddIsomorphismFromInternalHomToObject</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddIsomorphismFromInternalHomToObject</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">IsomorphismFromInternalHomToObject</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a ) \mapsto \mathtt{IsomorphismFromInternalHomToObject}(a)</span>.</p>

<p><a id="X7D6421147BF6651B" name="X7D6421147BF6651B"></a></p>

<h5>1.14-40 AddIsomorphismFromInternalHomToObjectWithGivenInternalHom</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddIsomorphismFromInternalHomToObjectWithGivenInternalHom</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddIsomorphismFromInternalHomToObjectWithGivenInternalHom</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">IsomorphismFromInternalHomToObjectWithGivenInternalHom</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, s ) \mapsto \mathtt{IsomorphismFromInternalHomToObjectWithGivenInternalHom}(a, s)</span>.</p>

<p><a id="X82538F687DE872DD" name="X82538F687DE872DD"></a></p>

<h5>1.14-41 AddIsomorphismFromObjectToInternalHom</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddIsomorphismFromObjectToInternalHom</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddIsomorphismFromObjectToInternalHom</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">IsomorphismFromObjectToInternalHom</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a ) \mapsto \mathtt{IsomorphismFromObjectToInternalHom}(a)</span>.</p>

<p><a id="X78ED7FCC83D091AB" name="X78ED7FCC83D091AB"></a></p>

<h5>1.14-42 AddIsomorphismFromObjectToInternalHomWithGivenInternalHom</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddIsomorphismFromObjectToInternalHomWithGivenInternalHom</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddIsomorphismFromObjectToInternalHomWithGivenInternalHom</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">IsomorphismFromObjectToInternalHomWithGivenInternalHom</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, r ) \mapsto \mathtt{IsomorphismFromObjectToInternalHomWithGivenInternalHom}(a, r)</span>.</p>

<p><a id="X8406FBCD7EE968FF" name="X8406FBCD7EE968FF"></a></p>

<h5>1.14-43 AddLambdaElimination</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLambdaElimination</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLambdaElimination</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LambdaElimination</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b, alpha ) \mapsto \mathtt{LambdaElimination}(a, b, alpha)</span>.</p>

<p><a id="X84944B6283F2802A" name="X84944B6283F2802A"></a></p>

<h5>1.14-44 AddLambdaIntroduction</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLambdaIntroduction</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLambdaIntroduction</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LambdaIntroduction</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( alpha ) \mapsto \mathtt{LambdaIntroduction}(alpha)</span>.</p>

<p><a id="X843DC64486CB2ED1" name="X843DC64486CB2ED1"></a></p>

<h5>1.14-45 AddMonoidalPostComposeMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddMonoidalPostComposeMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddMonoidalPostComposeMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">MonoidalPostComposeMorphism</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b, c ) \mapsto \mathtt{MonoidalPostComposeMorphism}(a, b, c)</span>.</p>

<p><a id="X7FC3725A7CF804F9" name="X7FC3725A7CF804F9"></a></p>

<h5>1.14-46 AddMonoidalPostComposeMorphismWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddMonoidalPostComposeMorphismWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddMonoidalPostComposeMorphismWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">MonoidalPostComposeMorphismWithGivenObjects</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( s, a, b, c, r ) \mapsto \mathtt{MonoidalPostComposeMorphismWithGivenObjects}(s, a, b, c, r)</span>.</p>

<p><a id="X7B0C198782C01CBA" name="X7B0C198782C01CBA"></a></p>

<h5>1.14-47 AddMonoidalPreComposeMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddMonoidalPreComposeMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddMonoidalPreComposeMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">MonoidalPreComposeMorphism</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b, c ) \mapsto \mathtt{MonoidalPreComposeMorphism}(a, b, c)</span>.</p>

<p><a id="X7A22CD657A2A338C" name="X7A22CD657A2A338C"></a></p>

<h5>1.14-48 AddMonoidalPreComposeMorphismWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddMonoidalPreComposeMorphismWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddMonoidalPreComposeMorphismWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">MonoidalPreComposeMorphismWithGivenObjects</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( s, a, b, c, r ) \mapsto \mathtt{MonoidalPreComposeMorphismWithGivenObjects}(s, a, b, c, r)</span>.</p>

<p><a id="X7CF664D87D8D5CA1" name="X7CF664D87D8D5CA1"></a></p>

<h5>1.14-49 AddMorphismFromTensorProductToInternalHom</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddMorphismFromTensorProductToInternalHom</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddMorphismFromTensorProductToInternalHom</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">MorphismFromTensorProductToInternalHom</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b ) \mapsto \mathtt{MorphismFromTensorProductToInternalHom}(a, b)</span>.</p>

<p><a id="X86D3AF4A80FA738D" name="X86D3AF4A80FA738D"></a></p>

<h5>1.14-50 AddMorphismFromTensorProductToInternalHomWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddMorphismFromTensorProductToInternalHomWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddMorphismFromTensorProductToInternalHomWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">MorphismFromTensorProductToInternalHomWithGivenObjects</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( s, a, b, r ) \mapsto \mathtt{MorphismFromTensorProductToInternalHomWithGivenObjects}(s, a, b, r)</span>.</p>

<p><a id="X864B98B08041EE6C" name="X864B98B08041EE6C"></a></p>

<h5>1.14-51 AddMorphismToBidual</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddMorphismToBidual</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddMorphismToBidual</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">MorphismToBidual</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a ) \mapsto \mathtt{MorphismToBidual}(a)</span>.</p>

<p><a id="X84C05B087EFCE599" name="X84C05B087EFCE599"></a></p>

<h5>1.14-52 AddMorphismToBidualWithGivenBidual</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddMorphismToBidualWithGivenBidual</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddMorphismToBidualWithGivenBidual</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">MorphismToBidualWithGivenBidual</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, r ) \mapsto \mathtt{MorphismToBidualWithGivenBidual}(a, r)</span>.</p>

<p><a id="X7A020DBF860317F5" name="X7A020DBF860317F5"></a></p>

<h5>1.14-53 AddTensorProductDualityCompatibilityMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddTensorProductDualityCompatibilityMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddTensorProductDualityCompatibilityMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">TensorProductDualityCompatibilityMorphism</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b ) \mapsto \mathtt{TensorProductDualityCompatibilityMorphism}(a, b)</span>.</p>

<p><a id="X78D1B6AF8654A950" name="X78D1B6AF8654A950"></a></p>

<h5>1.14-54 AddTensorProductDualityCompatibilityMorphismWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddTensorProductDualityCompatibilityMorphismWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddTensorProductDualityCompatibilityMorphismWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">TensorProductDualityCompatibilityMorphismWithGivenObjects</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( s, a, b, r ) \mapsto \mathtt{TensorProductDualityCompatibilityMorphismWithGivenObjects}(s, a, b, r)</span>.</p>

<p><a id="X83A6EF0B7ED71EED" name="X83A6EF0B7ED71EED"></a></p>

<h5>1.14-55 AddTensorProductInternalHomCompatibilityMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddTensorProductInternalHomCompatibilityMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddTensorProductInternalHomCompatibilityMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">TensorProductInternalHomCompatibilityMorphism</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( list ) \mapsto \mathtt{TensorProductInternalHomCompatibilityMorphism}(list)</span>.</p>

<p><a id="X871C6B55843A0AF3" name="X871C6B55843A0AF3"></a></p>

<h5>1.14-56 AddTensorProductInternalHomCompatibilityMorphismWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddTensorProductInternalHomCompatibilityMorphismWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddTensorProductInternalHomCompatibilityMorphismWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">TensorProductInternalHomCompatibilityMorphismWithGivenObjects</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( source, list, range ) \mapsto \mathtt{TensorProductInternalHomCompatibilityMorphismWithGivenObjects}(source, list, range)</span>.</p>

<p><a id="X817EAD878544BF68" name="X817EAD878544BF68"></a></p>

<h5>1.14-57 AddTensorProductToInternalHomLeftAdjunctMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddTensorProductToInternalHomLeftAdjunctMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddTensorProductToInternalHomLeftAdjunctMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">TensorProductToInternalHomLeftAdjunctMorphism</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b, f ) \mapsto \mathtt{TensorProductToInternalHomLeftAdjunctMorphism}(a, b, f)</span>.</p>

<p><a id="X7B2FEF0985C2FACE" name="X7B2FEF0985C2FACE"></a></p>

<h5>1.14-58 AddTensorProductToInternalHomLeftAdjunctMorphismWithGivenInternalHom</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddTensorProductToInternalHomLeftAdjunctMorphismWithGivenInternalHom</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddTensorProductToInternalHomLeftAdjunctMorphismWithGivenInternalHom</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">TensorProductToInternalHomLeftAdjunctMorphismWithGivenInternalHom</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b, f, i ) \mapsto \mathtt{TensorProductToInternalHomLeftAdjunctMorphismWithGivenInternalHom}(a, b, f, i)</span>.</p>

<p><a id="X85A8D11983750164" name="X85A8D11983750164"></a></p>

<h5>1.14-59 AddTensorProductToInternalHomLeftAdjunctionIsomorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddTensorProductToInternalHomLeftAdjunctionIsomorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddTensorProductToInternalHomLeftAdjunctionIsomorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">TensorProductToInternalHomLeftAdjunctionIsomorphism</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b, c ) \mapsto \mathtt{TensorProductToInternalHomLeftAdjunctionIsomorphism}(a, b, c)</span>.</p>

<p><a id="X7AE873FD87E4B12D" name="X7AE873FD87E4B12D"></a></p>

<h5>1.14-60 AddTensorProductToInternalHomLeftAdjunctionIsomorphismWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddTensorProductToInternalHomLeftAdjunctionIsomorphismWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddTensorProductToInternalHomLeftAdjunctionIsomorphismWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">TensorProductToInternalHomLeftAdjunctionIsomorphismWithGivenObjects</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( s, a, b, c, r ) \mapsto \mathtt{TensorProductToInternalHomLeftAdjunctionIsomorphismWithGivenObjects}(s, a, b, c, r)</span>.</p>

<p><a id="X7AF5FBEE859787CB" name="X7AF5FBEE859787CB"></a></p>

<h5>1.14-61 AddTensorProductToInternalHomRightAdjunctMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddTensorProductToInternalHomRightAdjunctMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddTensorProductToInternalHomRightAdjunctMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">TensorProductToInternalHomRightAdjunctMorphism</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b, f ) \mapsto \mathtt{TensorProductToInternalHomRightAdjunctMorphism}(a, b, f)</span>.</p>

<p><a id="X86B3F2BF813AFBDA" name="X86B3F2BF813AFBDA"></a></p>

<h5>1.14-62 AddTensorProductToInternalHomRightAdjunctMorphismWithGivenInternalHom</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddTensorProductToInternalHomRightAdjunctMorphismWithGivenInternalHom</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddTensorProductToInternalHomRightAdjunctMorphismWithGivenInternalHom</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">TensorProductToInternalHomRightAdjunctMorphismWithGivenInternalHom</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b, f, i ) \mapsto \mathtt{TensorProductToInternalHomRightAdjunctMorphismWithGivenInternalHom}(a, b, f, i)</span>.</p>

<p><a id="X79777C5F825C788E" name="X79777C5F825C788E"></a></p>

<h5>1.14-63 AddTensorProductToInternalHomRightAdjunctionIsomorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddTensorProductToInternalHomRightAdjunctionIsomorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddTensorProductToInternalHomRightAdjunctionIsomorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">TensorProductToInternalHomRightAdjunctionIsomorphism</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b, c ) \mapsto \mathtt{TensorProductToInternalHomRightAdjunctionIsomorphism}(a, b, c)</span>.</p>

<p><a id="X86FD5F8A83CE2A59" name="X86FD5F8A83CE2A59"></a></p>

<h5>1.14-64 AddTensorProductToInternalHomRightAdjunctionIsomorphismWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddTensorProductToInternalHomRightAdjunctionIsomorphismWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddTensorProductToInternalHomRightAdjunctionIsomorphismWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">TensorProductToInternalHomRightAdjunctionIsomorphismWithGivenObjects</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( s, a, b, c, r ) \mapsto \mathtt{TensorProductToInternalHomRightAdjunctionIsomorphismWithGivenObjects}(s, a, b, c, r)</span>.</p>

<p><a id="X7FCEDB3B7DF69A1E" name="X7FCEDB3B7DF69A1E"></a></p>

<h5>1.14-65 AddUniversalPropertyOfDual</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddUniversalPropertyOfDual</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddUniversalPropertyOfDual</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">UniversalPropertyOfDual</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( t, a, alpha ) \mapsto \mathtt{UniversalPropertyOfDual}(t, a, alpha)</span>.</p>

<p><a id="X7D23088385F021AA" name="X7D23088385F021AA"></a></p>

<h5>1.14-66 AddCoDualOnMorphisms</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddCoDualOnMorphisms</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddCoDualOnMorphisms</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">CoDualOnMorphisms</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( alpha ) \mapsto \mathtt{CoDualOnMorphisms}(alpha)</span>.</p>

<p><a id="X7C2568FD82259231" name="X7C2568FD82259231"></a></p>

<h5>1.14-67 AddCoDualOnMorphismsWithGivenCoDuals</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddCoDualOnMorphismsWithGivenCoDuals</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddCoDualOnMorphismsWithGivenCoDuals</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">CoDualOnMorphismsWithGivenCoDuals</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( s, alpha, r ) \mapsto \mathtt{CoDualOnMorphismsWithGivenCoDuals}(s, alpha, r)</span>.</p>

<p><a id="X7C1CDE7F855ACB74" name="X7C1CDE7F855ACB74"></a></p>

<h5>1.14-68 AddCoDualOnObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddCoDualOnObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddCoDualOnObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">CoDualOnObjects</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a ) \mapsto \mathtt{CoDualOnObjects}(a)</span>.</p>

<p><a id="X7D9B355D8261CB17" name="X7D9B355D8261CB17"></a></p>

<h5>1.14-69 AddCoDualityTensorProductCompatibilityMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddCoDualityTensorProductCompatibilityMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddCoDualityTensorProductCompatibilityMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">CoDualityTensorProductCompatibilityMorphism</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b ) \mapsto \mathtt{CoDualityTensorProductCompatibilityMorphism}(a, b)</span>.</p>

<p><a id="X7CE8010980DBA597" name="X7CE8010980DBA597"></a></p>

<h5>1.14-70 AddCoDualityTensorProductCompatibilityMorphismWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddCoDualityTensorProductCompatibilityMorphismWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddCoDualityTensorProductCompatibilityMorphismWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">CoDualityTensorProductCompatibilityMorphismWithGivenObjects</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( s, a, b, r ) \mapsto \mathtt{CoDualityTensorProductCompatibilityMorphismWithGivenObjects}(s, a, b, r)</span>.</p>

<p><a id="X7E7962CC7E809023" name="X7E7962CC7E809023"></a></p>

<h5>1.14-71 AddCoLambdaElimination</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddCoLambdaElimination</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddCoLambdaElimination</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">CoLambdaElimination</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b, alpha ) \mapsto \mathtt{CoLambdaElimination}(a, b, alpha)</span>.</p>

<p><a id="X7C3868657D8A0400" name="X7C3868657D8A0400"></a></p>

<h5>1.14-72 AddCoLambdaIntroduction</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddCoLambdaIntroduction</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddCoLambdaIntroduction</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">CoLambdaIntroduction</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( alpha ) \mapsto \mathtt{CoLambdaIntroduction}(alpha)</span>.</p>

<p><a id="X839204FD79F2968D" name="X839204FD79F2968D"></a></p>

<h5>1.14-73 AddCoclosedEvaluationForCoDual</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddCoclosedEvaluationForCoDual</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddCoclosedEvaluationForCoDual</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">CoclosedEvaluationForCoDual</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a ) \mapsto \mathtt{CoclosedEvaluationForCoDual}(a)</span>.</p>

<p><a id="X803976DB7C8F307C" name="X803976DB7C8F307C"></a></p>

<h5>1.14-74 AddCoclosedEvaluationForCoDualWithGivenTensorProduct</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddCoclosedEvaluationForCoDualWithGivenTensorProduct</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddCoclosedEvaluationForCoDualWithGivenTensorProduct</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">CoclosedEvaluationForCoDualWithGivenTensorProduct</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( s, a, r ) \mapsto \mathtt{CoclosedEvaluationForCoDualWithGivenTensorProduct}(s, a, r)</span>.</p>

<p><a id="X829CAF887FAC5BF0" name="X829CAF887FAC5BF0"></a></p>

<h5>1.14-75 AddCoclosedMonoidalLeftCoevaluationMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddCoclosedMonoidalLeftCoevaluationMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddCoclosedMonoidalLeftCoevaluationMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">CoclosedMonoidalLeftCoevaluationMorphism</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b ) \mapsto \mathtt{CoclosedMonoidalLeftCoevaluationMorphism}(a, b)</span>.</p>

<p><a id="X7E7EBA4381366E7A" name="X7E7EBA4381366E7A"></a></p>

<h5>1.14-76 AddCoclosedMonoidalLeftCoevaluationMorphismWithGivenSource</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddCoclosedMonoidalLeftCoevaluationMorphismWithGivenSource</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddCoclosedMonoidalLeftCoevaluationMorphismWithGivenSource</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">CoclosedMonoidalLeftCoevaluationMorphismWithGivenSource</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b, s ) \mapsto \mathtt{CoclosedMonoidalLeftCoevaluationMorphismWithGivenSource}(a, b, s)</span>.</p>

<p><a id="X81EC6B3E80876BC8" name="X81EC6B3E80876BC8"></a></p>

<h5>1.14-77 AddCoclosedMonoidalLeftEvaluationMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddCoclosedMonoidalLeftEvaluationMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddCoclosedMonoidalLeftEvaluationMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">CoclosedMonoidalLeftEvaluationMorphism</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b ) \mapsto \mathtt{CoclosedMonoidalLeftEvaluationMorphism}(a, b)</span>.</p>

<p><a id="X839DE15C87358F99" name="X839DE15C87358F99"></a></p>

<h5>1.14-78 AddCoclosedMonoidalLeftEvaluationMorphismWithGivenRange</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddCoclosedMonoidalLeftEvaluationMorphismWithGivenRange</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddCoclosedMonoidalLeftEvaluationMorphismWithGivenRange</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">CoclosedMonoidalLeftEvaluationMorphismWithGivenRange</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b, r ) \mapsto \mathtt{CoclosedMonoidalLeftEvaluationMorphismWithGivenRange}(a, b, r)</span>.</p>

<p><a id="X78A8CB687ADC4653" name="X78A8CB687ADC4653"></a></p>

<h5>1.14-79 AddCoclosedMonoidalRightCoevaluationMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddCoclosedMonoidalRightCoevaluationMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddCoclosedMonoidalRightCoevaluationMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">CoclosedMonoidalRightCoevaluationMorphism</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b ) \mapsto \mathtt{CoclosedMonoidalRightCoevaluationMorphism}(a, b)</span>.</p>

<p><a id="X783C75CD79B2E8C9" name="X783C75CD79B2E8C9"></a></p>

<h5>1.14-80 AddCoclosedMonoidalRightCoevaluationMorphismWithGivenSource</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddCoclosedMonoidalRightCoevaluationMorphismWithGivenSource</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddCoclosedMonoidalRightCoevaluationMorphismWithGivenSource</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">CoclosedMonoidalRightCoevaluationMorphismWithGivenSource</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b, s ) \mapsto \mathtt{CoclosedMonoidalRightCoevaluationMorphismWithGivenSource}(a, b, s)</span>.</p>

<p><a id="X85F82B2F84E55DD2" name="X85F82B2F84E55DD2"></a></p>

<h5>1.14-81 AddCoclosedMonoidalRightEvaluationMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddCoclosedMonoidalRightEvaluationMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddCoclosedMonoidalRightEvaluationMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">CoclosedMonoidalRightEvaluationMorphism</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b ) \mapsto \mathtt{CoclosedMonoidalRightEvaluationMorphism}(a, b)</span>.</p>

<p><a id="X86DC2EF07B421CE0" name="X86DC2EF07B421CE0"></a></p>

<h5>1.14-82 AddCoclosedMonoidalRightEvaluationMorphismWithGivenRange</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddCoclosedMonoidalRightEvaluationMorphismWithGivenRange</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddCoclosedMonoidalRightEvaluationMorphismWithGivenRange</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">CoclosedMonoidalRightEvaluationMorphismWithGivenRange</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b, r ) \mapsto \mathtt{CoclosedMonoidalRightEvaluationMorphismWithGivenRange}(a, b, r)</span>.</p>

<p><a id="X7D63C4A57A467DAA" name="X7D63C4A57A467DAA"></a></p>

<h5>1.14-83 AddInternalCoHomOnMorphisms</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddInternalCoHomOnMorphisms</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddInternalCoHomOnMorphisms</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">InternalCoHomOnMorphisms</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( alpha, beta ) \mapsto \mathtt{InternalCoHomOnMorphisms}(alpha, beta)</span>.</p>

<p><a id="X87A67CDD86E0CE05" name="X87A67CDD86E0CE05"></a></p>

<h5>1.14-84 AddInternalCoHomOnMorphismsWithGivenInternalCoHoms</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddInternalCoHomOnMorphismsWithGivenInternalCoHoms</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddInternalCoHomOnMorphismsWithGivenInternalCoHoms</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">InternalCoHomOnMorphismsWithGivenInternalCoHoms</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( s, alpha, beta, r ) \mapsto \mathtt{InternalCoHomOnMorphismsWithGivenInternalCoHoms}(s, alpha, beta, r)</span>.</p>

<p><a id="X828648F183570AE3" name="X828648F183570AE3"></a></p>

<h5>1.14-85 AddInternalCoHomOnObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddInternalCoHomOnObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddInternalCoHomOnObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">InternalCoHomOnObjects</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b ) \mapsto \mathtt{InternalCoHomOnObjects}(a, b)</span>.</p>

<p><a id="X78278696834ACA53" name="X78278696834ACA53"></a></p>

<h5>1.14-86 AddInternalCoHomTensorProductCompatibilityMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddInternalCoHomTensorProductCompatibilityMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddInternalCoHomTensorProductCompatibilityMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">InternalCoHomTensorProductCompatibilityMorphism</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( list ) \mapsto \mathtt{InternalCoHomTensorProductCompatibilityMorphism}(list)</span>.</p>

<p><a id="X82EA4C857C7BCC60" name="X82EA4C857C7BCC60"></a></p>

<h5>1.14-87 AddInternalCoHomTensorProductCompatibilityMorphismWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddInternalCoHomTensorProductCompatibilityMorphismWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddInternalCoHomTensorProductCompatibilityMorphismWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">InternalCoHomTensorProductCompatibilityMorphismWithGivenObjects</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( source, list, range ) \mapsto \mathtt{InternalCoHomTensorProductCompatibilityMorphismWithGivenObjects}(source, list, range)</span>.</p>

<p><a id="X7C7256EE79374540" name="X7C7256EE79374540"></a></p>

<h5>1.14-88 AddInternalCoHomToTensorProductLeftAdjunctMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddInternalCoHomToTensorProductLeftAdjunctMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddInternalCoHomToTensorProductLeftAdjunctMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">InternalCoHomToTensorProductLeftAdjunctMorphism</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, c, f ) \mapsto \mathtt{InternalCoHomToTensorProductLeftAdjunctMorphism}(a, c, f)</span>.</p>

<p><a id="X84EBD01D7843FAAD" name="X84EBD01D7843FAAD"></a></p>

<h5>1.14-89 AddInternalCoHomToTensorProductLeftAdjunctMorphismWithGivenTensorProduct</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddInternalCoHomToTensorProductLeftAdjunctMorphismWithGivenTensorProduct</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddInternalCoHomToTensorProductLeftAdjunctMorphismWithGivenTensorProduct</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">InternalCoHomToTensorProductLeftAdjunctMorphismWithGivenTensorProduct</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, c, f, t ) \mapsto \mathtt{InternalCoHomToTensorProductLeftAdjunctMorphismWithGivenTensorProduct}(a, c, f, t)</span>.</p>

<p><a id="X858ED26087369677" name="X858ED26087369677"></a></p>

<h5>1.14-90 AddInternalCoHomToTensorProductRightAdjunctMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddInternalCoHomToTensorProductRightAdjunctMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddInternalCoHomToTensorProductRightAdjunctMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">InternalCoHomToTensorProductRightAdjunctMorphism</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b, f ) \mapsto \mathtt{InternalCoHomToTensorProductRightAdjunctMorphism}(a, b, f)</span>.</p>

<p><a id="X7E97DAC0782AACEC" name="X7E97DAC0782AACEC"></a></p>

<h5>1.14-91 AddInternalCoHomToTensorProductRightAdjunctMorphismWithGivenTensorProduct</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddInternalCoHomToTensorProductRightAdjunctMorphismWithGivenTensorProduct</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddInternalCoHomToTensorProductRightAdjunctMorphismWithGivenTensorProduct</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">InternalCoHomToTensorProductRightAdjunctMorphismWithGivenTensorProduct</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b, f, t ) \mapsto \mathtt{InternalCoHomToTensorProductRightAdjunctMorphismWithGivenTensorProduct}(a, b, f, t)</span>.</p>

<p><a id="X7A2B14497B4924A7" name="X7A2B14497B4924A7"></a></p>

<h5>1.14-92 AddIsomorphismFromCoDualObjectToInternalCoHomFromTensorUnit</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddIsomorphismFromCoDualObjectToInternalCoHomFromTensorUnit</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddIsomorphismFromCoDualObjectToInternalCoHomFromTensorUnit</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">IsomorphismFromCoDualObjectToInternalCoHomFromTensorUnit</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a ) \mapsto \mathtt{IsomorphismFromCoDualObjectToInternalCoHomFromTensorUnit}(a)</span>.</p>

<p><a id="X8143326C7BE5E321" name="X8143326C7BE5E321"></a></p>

<h5>1.14-93 AddIsomorphismFromInternalCoHomFromTensorUnitToCoDualObject</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddIsomorphismFromInternalCoHomFromTensorUnitToCoDualObject</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddIsomorphismFromInternalCoHomFromTensorUnitToCoDualObject</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">IsomorphismFromInternalCoHomFromTensorUnitToCoDualObject</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a ) \mapsto \mathtt{IsomorphismFromInternalCoHomFromTensorUnitToCoDualObject}(a)</span>.</p>

<p><a id="X7C9F35A779395B26" name="X7C9F35A779395B26"></a></p>

<h5>1.14-94 AddIsomorphismFromInternalCoHomToObject</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddIsomorphismFromInternalCoHomToObject</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddIsomorphismFromInternalCoHomToObject</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">IsomorphismFromInternalCoHomToObject</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a ) \mapsto \mathtt{IsomorphismFromInternalCoHomToObject}(a)</span>.</p>

<p><a id="X7D0E88AC7C0304D3" name="X7D0E88AC7C0304D3"></a></p>

<h5>1.14-95 AddIsomorphismFromInternalCoHomToObjectWithGivenInternalCoHom</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddIsomorphismFromInternalCoHomToObjectWithGivenInternalCoHom</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddIsomorphismFromInternalCoHomToObjectWithGivenInternalCoHom</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">IsomorphismFromInternalCoHomToObjectWithGivenInternalCoHom</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, s ) \mapsto \mathtt{IsomorphismFromInternalCoHomToObjectWithGivenInternalCoHom}(a, s)</span>.</p>

<p><a id="X7E18F31C86620139" name="X7E18F31C86620139"></a></p>

<h5>1.14-96 AddIsomorphismFromObjectToInternalCoHom</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddIsomorphismFromObjectToInternalCoHom</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddIsomorphismFromObjectToInternalCoHom</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">IsomorphismFromObjectToInternalCoHom</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a ) \mapsto \mathtt{IsomorphismFromObjectToInternalCoHom}(a)</span>.</p>

<p><a id="X8304276383585ECC" name="X8304276383585ECC"></a></p>

<h5>1.14-97 AddIsomorphismFromObjectToInternalCoHomWithGivenInternalCoHom</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddIsomorphismFromObjectToInternalCoHomWithGivenInternalCoHom</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddIsomorphismFromObjectToInternalCoHomWithGivenInternalCoHom</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">IsomorphismFromObjectToInternalCoHomWithGivenInternalCoHom</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, r ) \mapsto \mathtt{IsomorphismFromObjectToInternalCoHomWithGivenInternalCoHom}(a, r)</span>.</p>

<p><a id="X7DE479077F155716" name="X7DE479077F155716"></a></p>

<h5>1.14-98 AddMonoidalPostCoComposeMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddMonoidalPostCoComposeMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddMonoidalPostCoComposeMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">MonoidalPostCoComposeMorphism</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b, c ) \mapsto \mathtt{MonoidalPostCoComposeMorphism}(a, b, c)</span>.</p>

<p><a id="X79858B577BD4F1E1" name="X79858B577BD4F1E1"></a></p>

<h5>1.14-99 AddMonoidalPostCoComposeMorphismWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddMonoidalPostCoComposeMorphismWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddMonoidalPostCoComposeMorphismWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">MonoidalPostCoComposeMorphismWithGivenObjects</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( s, a, b, c, r ) \mapsto \mathtt{MonoidalPostCoComposeMorphismWithGivenObjects}(s, a, b, c, r)</span>.</p>

<p><a id="X7D1662EA819EA1A2" name="X7D1662EA819EA1A2"></a></p>

<h5>1.14-100 AddMonoidalPreCoComposeMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddMonoidalPreCoComposeMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddMonoidalPreCoComposeMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">MonoidalPreCoComposeMorphism</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b, c ) \mapsto \mathtt{MonoidalPreCoComposeMorphism}(a, b, c)</span>.</p>

<p><a id="X81DFED7386A953E0" name="X81DFED7386A953E0"></a></p>

<h5>1.14-101 AddMonoidalPreCoComposeMorphismWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddMonoidalPreCoComposeMorphismWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddMonoidalPreCoComposeMorphismWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">MonoidalPreCoComposeMorphismWithGivenObjects</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( s, a, b, c, r ) \mapsto \mathtt{MonoidalPreCoComposeMorphismWithGivenObjects}(s, a, b, c, r)</span>.</p>

<p><a id="X7D1615257BAA311F" name="X7D1615257BAA311F"></a></p>

<h5>1.14-102 AddMorphismFromCoBidual</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddMorphismFromCoBidual</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddMorphismFromCoBidual</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">MorphismFromCoBidual</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a ) \mapsto \mathtt{MorphismFromCoBidual}(a)</span>.</p>

<p><a id="X84D1F74D8118B2A0" name="X84D1F74D8118B2A0"></a></p>

<h5>1.14-103 AddMorphismFromCoBidualWithGivenCoBidual</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddMorphismFromCoBidualWithGivenCoBidual</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddMorphismFromCoBidualWithGivenCoBidual</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">MorphismFromCoBidualWithGivenCoBidual</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, s ) \mapsto \mathtt{MorphismFromCoBidualWithGivenCoBidual}(a, s)</span>.</p>

<p><a id="X7C3C01F1834A4B9B" name="X7C3C01F1834A4B9B"></a></p>

<h5>1.14-104 AddMorphismFromInternalCoHomToTensorProduct</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddMorphismFromInternalCoHomToTensorProduct</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddMorphismFromInternalCoHomToTensorProduct</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">MorphismFromInternalCoHomToTensorProduct</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b ) \mapsto \mathtt{MorphismFromInternalCoHomToTensorProduct}(a, b)</span>.</p>

<p><a id="X87AB2C4D84F19F37" name="X87AB2C4D84F19F37"></a></p>

<h5>1.14-105 AddMorphismFromInternalCoHomToTensorProductWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddMorphismFromInternalCoHomToTensorProductWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddMorphismFromInternalCoHomToTensorProductWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">MorphismFromInternalCoHomToTensorProductWithGivenObjects</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( s, a, b, r ) \mapsto \mathtt{MorphismFromInternalCoHomToTensorProductWithGivenObjects}(s, a, b, r)</span>.</p>

<p><a id="X7C0E0CF87FEFEB0D" name="X7C0E0CF87FEFEB0D"></a></p>

<h5>1.14-106 AddTensorProductToInternalCoHomLeftAdjunctMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddTensorProductToInternalCoHomLeftAdjunctMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddTensorProductToInternalCoHomLeftAdjunctMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">TensorProductToInternalCoHomLeftAdjunctMorphism</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( b, c, g ) \mapsto \mathtt{TensorProductToInternalCoHomLeftAdjunctMorphism}(b, c, g)</span>.</p>

<p><a id="X7A838651781657DA" name="X7A838651781657DA"></a></p>

<h5>1.14-107 AddTensorProductToInternalCoHomLeftAdjunctMorphismWithGivenInternalCoHom</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddTensorProductToInternalCoHomLeftAdjunctMorphismWithGivenInternalCoHom</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddTensorProductToInternalCoHomLeftAdjunctMorphismWithGivenInternalCoHom</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">TensorProductToInternalCoHomLeftAdjunctMorphismWithGivenInternalCoHom</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( b, c, g, i ) \mapsto \mathtt{TensorProductToInternalCoHomLeftAdjunctMorphismWithGivenInternalCoHom}(b, c, g, i)</span>.</p>

<p><a id="X8123546E81EE383A" name="X8123546E81EE383A"></a></p>

<h5>1.14-108 AddTensorProductToInternalCoHomRightAdjunctMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddTensorProductToInternalCoHomRightAdjunctMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddTensorProductToInternalCoHomRightAdjunctMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">TensorProductToInternalCoHomRightAdjunctMorphism</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( b, c, g ) \mapsto \mathtt{TensorProductToInternalCoHomRightAdjunctMorphism}(b, c, g)</span>.</p>

<p><a id="X8698898584E99695" name="X8698898584E99695"></a></p>

<h5>1.14-109 AddTensorProductToInternalCoHomRightAdjunctMorphismWithGivenInternalCoHom</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddTensorProductToInternalCoHomRightAdjunctMorphismWithGivenInternalCoHom</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddTensorProductToInternalCoHomRightAdjunctMorphismWithGivenInternalCoHom</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">TensorProductToInternalCoHomRightAdjunctMorphismWithGivenInternalCoHom</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( b, c, g, i ) \mapsto \mathtt{TensorProductToInternalCoHomRightAdjunctMorphismWithGivenInternalCoHom}(b, c, g, i)</span>.</p>

<p><a id="X8519ECF17EC07916" name="X8519ECF17EC07916"></a></p>

<h5>1.14-110 AddUniversalPropertyOfCoDual</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddUniversalPropertyOfCoDual</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddUniversalPropertyOfCoDual</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">UniversalPropertyOfCoDual</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( t, a, alpha ) \mapsto \mathtt{UniversalPropertyOfCoDual}(t, a, alpha)</span>.</p>

<p><a id="X7F868E597F1C1AD7" name="X7F868E597F1C1AD7"></a></p>

<h5>1.14-111 AddIsomorphismFromLeftDualObjectToLeftInternalHomIntoTensorUnit</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddIsomorphismFromLeftDualObjectToLeftInternalHomIntoTensorUnit</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddIsomorphismFromLeftDualObjectToLeftInternalHomIntoTensorUnit</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">IsomorphismFromLeftDualObjectToLeftInternalHomIntoTensorUnit</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a ) \mapsto \mathtt{IsomorphismFromLeftDualObjectToLeftInternalHomIntoTensorUnit}(a)</span>.</p>

<p><a id="X810B50C27901021C" name="X810B50C27901021C"></a></p>

<h5>1.14-112 AddIsomorphismFromLeftInternalHomIntoTensorUnitToLeftDualObject</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddIsomorphismFromLeftInternalHomIntoTensorUnitToLeftDualObject</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddIsomorphismFromLeftInternalHomIntoTensorUnitToLeftDualObject</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">IsomorphismFromLeftInternalHomIntoTensorUnitToLeftDualObject</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a ) \mapsto \mathtt{IsomorphismFromLeftInternalHomIntoTensorUnitToLeftDualObject}(a)</span>.</p>

<p><a id="X87415032853E8340" name="X87415032853E8340"></a></p>

<h5>1.14-113 AddIsomorphismFromLeftInternalHomToObject</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddIsomorphismFromLeftInternalHomToObject</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddIsomorphismFromLeftInternalHomToObject</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">IsomorphismFromLeftInternalHomToObject</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a ) \mapsto \mathtt{IsomorphismFromLeftInternalHomToObject}(a)</span>.</p>

<p><a id="X83DAADEE8139DACA" name="X83DAADEE8139DACA"></a></p>

<h5>1.14-114 AddIsomorphismFromLeftInternalHomToObjectWithGivenLeftInternalHom</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddIsomorphismFromLeftInternalHomToObjectWithGivenLeftInternalHom</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddIsomorphismFromLeftInternalHomToObjectWithGivenLeftInternalHom</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">IsomorphismFromLeftInternalHomToObjectWithGivenLeftInternalHom</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, s ) \mapsto \mathtt{IsomorphismFromLeftInternalHomToObjectWithGivenLeftInternalHom}(a, s)</span>.</p>

<p><a id="X7FA337D07BCD9D5B" name="X7FA337D07BCD9D5B"></a></p>

<h5>1.14-115 AddIsomorphismFromObjectToLeftInternalHom</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddIsomorphismFromObjectToLeftInternalHom</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddIsomorphismFromObjectToLeftInternalHom</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">IsomorphismFromObjectToLeftInternalHom</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a ) \mapsto \mathtt{IsomorphismFromObjectToLeftInternalHom}(a)</span>.</p>

<p><a id="X7EA7B1777FCAC4D1" name="X7EA7B1777FCAC4D1"></a></p>

<h5>1.14-116 AddIsomorphismFromObjectToLeftInternalHomWithGivenLeftInternalHom</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddIsomorphismFromObjectToLeftInternalHomWithGivenLeftInternalHom</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddIsomorphismFromObjectToLeftInternalHomWithGivenLeftInternalHom</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">IsomorphismFromObjectToLeftInternalHomWithGivenLeftInternalHom</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, r ) \mapsto \mathtt{IsomorphismFromObjectToLeftInternalHomWithGivenLeftInternalHom}(a, r)</span>.</p>

<p><a id="X7D1E4F66851991AB" name="X7D1E4F66851991AB"></a></p>

<h5>1.14-117 AddLeftClosedMonoidalCoevaluationMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftClosedMonoidalCoevaluationMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftClosedMonoidalCoevaluationMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LeftClosedMonoidalCoevaluationMorphism</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b ) \mapsto \mathtt{LeftClosedMonoidalCoevaluationMorphism}(a, b)</span>.</p>

<p><a id="X7EF0D5B782AB75FA" name="X7EF0D5B782AB75FA"></a></p>

<h5>1.14-118 AddLeftClosedMonoidalCoevaluationMorphismWithGivenRange</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftClosedMonoidalCoevaluationMorphismWithGivenRange</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftClosedMonoidalCoevaluationMorphismWithGivenRange</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LeftClosedMonoidalCoevaluationMorphismWithGivenRange</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b, r ) \mapsto \mathtt{LeftClosedMonoidalCoevaluationMorphismWithGivenRange}(a, b, r)</span>.</p>

<p><a id="X7FD8142C7CBF7FB1" name="X7FD8142C7CBF7FB1"></a></p>

<h5>1.14-119 AddLeftClosedMonoidalEvaluationForLeftDual</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftClosedMonoidalEvaluationForLeftDual</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftClosedMonoidalEvaluationForLeftDual</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LeftClosedMonoidalEvaluationForLeftDual</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a ) \mapsto \mathtt{LeftClosedMonoidalEvaluationForLeftDual}(a)</span>.</p>

<p><a id="X7A89130185CCF31D" name="X7A89130185CCF31D"></a></p>

<h5>1.14-120 AddLeftClosedMonoidalEvaluationForLeftDualWithGivenTensorProduct</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftClosedMonoidalEvaluationForLeftDualWithGivenTensorProduct</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftClosedMonoidalEvaluationForLeftDualWithGivenTensorProduct</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LeftClosedMonoidalEvaluationForLeftDualWithGivenTensorProduct</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( s, a, r ) \mapsto \mathtt{LeftClosedMonoidalEvaluationForLeftDualWithGivenTensorProduct}(s, a, r)</span>.</p>

<p><a id="X7D75530C7E938B81" name="X7D75530C7E938B81"></a></p>

<h5>1.14-121 AddLeftClosedMonoidalEvaluationMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftClosedMonoidalEvaluationMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftClosedMonoidalEvaluationMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LeftClosedMonoidalEvaluationMorphism</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b ) \mapsto \mathtt{LeftClosedMonoidalEvaluationMorphism}(a, b)</span>.</p>

<p><a id="X8535FD8E7894236B" name="X8535FD8E7894236B"></a></p>

<h5>1.14-122 AddLeftClosedMonoidalEvaluationMorphismWithGivenSource</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftClosedMonoidalEvaluationMorphismWithGivenSource</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftClosedMonoidalEvaluationMorphismWithGivenSource</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LeftClosedMonoidalEvaluationMorphismWithGivenSource</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b, s ) \mapsto \mathtt{LeftClosedMonoidalEvaluationMorphismWithGivenSource}(a, b, s)</span>.</p>

<p><a id="X869B3FD87FC09E21" name="X869B3FD87FC09E21"></a></p>

<h5>1.14-123 AddLeftClosedMonoidalLambdaElimination</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftClosedMonoidalLambdaElimination</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftClosedMonoidalLambdaElimination</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LeftClosedMonoidalLambdaElimination</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b, alpha ) \mapsto \mathtt{LeftClosedMonoidalLambdaElimination}(a, b, alpha)</span>.</p>

<p><a id="X7CC085AB7DBC581A" name="X7CC085AB7DBC581A"></a></p>

<h5>1.14-124 AddLeftClosedMonoidalLambdaIntroduction</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftClosedMonoidalLambdaIntroduction</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftClosedMonoidalLambdaIntroduction</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LeftClosedMonoidalLambdaIntroduction</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( alpha ) \mapsto \mathtt{LeftClosedMonoidalLambdaIntroduction}(alpha)</span>.</p>

<p><a id="X7BE971CB7E989544" name="X7BE971CB7E989544"></a></p>

<h5>1.14-125 AddLeftClosedMonoidalPostComposeMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftClosedMonoidalPostComposeMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftClosedMonoidalPostComposeMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LeftClosedMonoidalPostComposeMorphism</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b, c ) \mapsto \mathtt{LeftClosedMonoidalPostComposeMorphism}(a, b, c)</span>.</p>

<p><a id="X7B6DBF17796A971A" name="X7B6DBF17796A971A"></a></p>

<h5>1.14-126 AddLeftClosedMonoidalPostComposeMorphismWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftClosedMonoidalPostComposeMorphismWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftClosedMonoidalPostComposeMorphismWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LeftClosedMonoidalPostComposeMorphismWithGivenObjects</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( s, a, b, c, r ) \mapsto \mathtt{LeftClosedMonoidalPostComposeMorphismWithGivenObjects}(s, a, b, c, r)</span>.</p>

<p><a id="X799401467830D201" name="X799401467830D201"></a></p>

<h5>1.14-127 AddLeftClosedMonoidalPreComposeMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftClosedMonoidalPreComposeMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftClosedMonoidalPreComposeMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LeftClosedMonoidalPreComposeMorphism</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b, c ) \mapsto \mathtt{LeftClosedMonoidalPreComposeMorphism}(a, b, c)</span>.</p>

<p><a id="X7915D4437C9257A5" name="X7915D4437C9257A5"></a></p>

<h5>1.14-128 AddLeftClosedMonoidalPreComposeMorphismWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftClosedMonoidalPreComposeMorphismWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftClosedMonoidalPreComposeMorphismWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LeftClosedMonoidalPreComposeMorphismWithGivenObjects</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( s, a, b, c, r ) \mapsto \mathtt{LeftClosedMonoidalPreComposeMorphismWithGivenObjects}(s, a, b, c, r)</span>.</p>

<p><a id="X79D85C017917C1D4" name="X79D85C017917C1D4"></a></p>

<h5>1.14-129 AddLeftDualOnMorphisms</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftDualOnMorphisms</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftDualOnMorphisms</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LeftDualOnMorphisms</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( alpha ) \mapsto \mathtt{LeftDualOnMorphisms}(alpha)</span>.</p>

<p><a id="X816C625A82BCDDE3" name="X816C625A82BCDDE3"></a></p>

<h5>1.14-130 AddLeftDualOnMorphismsWithGivenLeftDuals</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftDualOnMorphismsWithGivenLeftDuals</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftDualOnMorphismsWithGivenLeftDuals</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LeftDualOnMorphismsWithGivenLeftDuals</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( s, alpha, r ) \mapsto \mathtt{LeftDualOnMorphismsWithGivenLeftDuals}(s, alpha, r)</span>.</p>

<p><a id="X7CB93B6E8555359D" name="X7CB93B6E8555359D"></a></p>

<h5>1.14-131 AddLeftDualOnObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftDualOnObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftDualOnObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LeftDualOnObjects</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a ) \mapsto \mathtt{LeftDualOnObjects}(a)</span>.</p>

<p><a id="X79B3B2F586530EFF" name="X79B3B2F586530EFF"></a></p>

<h5>1.14-132 AddLeftInternalHomOnMorphisms</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftInternalHomOnMorphisms</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftInternalHomOnMorphisms</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LeftInternalHomOnMorphisms</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( alpha, beta ) \mapsto \mathtt{LeftInternalHomOnMorphisms}(alpha, beta)</span>.</p>

<p><a id="X7DDC722B78B659A2" name="X7DDC722B78B659A2"></a></p>

<h5>1.14-133 AddLeftInternalHomOnMorphismsWithGivenLeftInternalHoms</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftInternalHomOnMorphismsWithGivenLeftInternalHoms</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftInternalHomOnMorphismsWithGivenLeftInternalHoms</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LeftInternalHomOnMorphismsWithGivenLeftInternalHoms</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( s, alpha, beta, r ) \mapsto \mathtt{LeftInternalHomOnMorphismsWithGivenLeftInternalHoms}(s, alpha, beta, r)</span>.</p>

<p><a id="X7FCF9DEA7F6B73F9" name="X7FCF9DEA7F6B73F9"></a></p>

<h5>1.14-134 AddLeftInternalHomOnObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftInternalHomOnObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftInternalHomOnObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LeftInternalHomOnObjects</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b ) \mapsto \mathtt{LeftInternalHomOnObjects}(a, b)</span>.</p>

<p><a id="X7F5EAC1E8104166E" name="X7F5EAC1E8104166E"></a></p>

<h5>1.14-135 AddLeftInternalHomToTensorProductAdjunctMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftInternalHomToTensorProductAdjunctMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftInternalHomToTensorProductAdjunctMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LeftInternalHomToTensorProductAdjunctMorphism</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( b, c, g ) \mapsto \mathtt{LeftInternalHomToTensorProductAdjunctMorphism}(b, c, g)</span>.</p>

<p><a id="X7C437ED77E95B84B" name="X7C437ED77E95B84B"></a></p>

<h5>1.14-136 AddLeftInternalHomToTensorProductAdjunctMorphismWithGivenTensorProduct</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftInternalHomToTensorProductAdjunctMorphismWithGivenTensorProduct</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftInternalHomToTensorProductAdjunctMorphismWithGivenTensorProduct</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LeftInternalHomToTensorProductAdjunctMorphismWithGivenTensorProduct</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( b, c, g, t ) \mapsto \mathtt{LeftInternalHomToTensorProductAdjunctMorphismWithGivenTensorProduct}(b, c, g, t)</span>.</p>

<p><a id="X7CA082FF7B01D8FB" name="X7CA082FF7B01D8FB"></a></p>

<h5>1.14-137 AddMorphismFromTensorProductToLeftInternalHom</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddMorphismFromTensorProductToLeftInternalHom</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddMorphismFromTensorProductToLeftInternalHom</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">MorphismFromTensorProductToLeftInternalHom</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b ) \mapsto \mathtt{MorphismFromTensorProductToLeftInternalHom}(a, b)</span>.</p>

<p><a id="X8028DDA77A2AF1D0" name="X8028DDA77A2AF1D0"></a></p>

<h5>1.14-138 AddMorphismFromTensorProductToLeftInternalHomWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddMorphismFromTensorProductToLeftInternalHomWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddMorphismFromTensorProductToLeftInternalHomWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">MorphismFromTensorProductToLeftInternalHomWithGivenObjects</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( s, a, b, r ) \mapsto \mathtt{MorphismFromTensorProductToLeftInternalHomWithGivenObjects}(s, a, b, r)</span>.</p>

<p><a id="X80EC71197C2C11D1" name="X80EC71197C2C11D1"></a></p>

<h5>1.14-139 AddMorphismToLeftBidual</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddMorphismToLeftBidual</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddMorphismToLeftBidual</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">MorphismToLeftBidual</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a ) \mapsto \mathtt{MorphismToLeftBidual}(a)</span>.</p>

<p><a id="X869265BC78942371" name="X869265BC78942371"></a></p>

<h5>1.14-140 AddMorphismToLeftBidualWithGivenLeftBidual</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddMorphismToLeftBidualWithGivenLeftBidual</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddMorphismToLeftBidualWithGivenLeftBidual</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">MorphismToLeftBidualWithGivenLeftBidual</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, r ) \mapsto \mathtt{MorphismToLeftBidualWithGivenLeftBidual}(a, r)</span>.</p>

<p><a id="X7953DC1F805D8C1A" name="X7953DC1F805D8C1A"></a></p>

<h5>1.14-141 AddTensorProductLeftDualityCompatibilityMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddTensorProductLeftDualityCompatibilityMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddTensorProductLeftDualityCompatibilityMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">TensorProductLeftDualityCompatibilityMorphism</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b ) \mapsto \mathtt{TensorProductLeftDualityCompatibilityMorphism}(a, b)</span>.</p>

<p><a id="X836F9F347AB09804" name="X836F9F347AB09804"></a></p>

<h5>1.14-142 AddTensorProductLeftDualityCompatibilityMorphismWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddTensorProductLeftDualityCompatibilityMorphismWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddTensorProductLeftDualityCompatibilityMorphismWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">TensorProductLeftDualityCompatibilityMorphismWithGivenObjects</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( s, a, b, r ) \mapsto \mathtt{TensorProductLeftDualityCompatibilityMorphismWithGivenObjects}(s, a, b, r)</span>.</p>

<p><a id="X7A76B21F7DD29DD4" name="X7A76B21F7DD29DD4"></a></p>

<h5>1.14-143 AddTensorProductLeftInternalHomCompatibilityMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddTensorProductLeftInternalHomCompatibilityMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddTensorProductLeftInternalHomCompatibilityMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">TensorProductLeftInternalHomCompatibilityMorphism</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( list ) \mapsto \mathtt{TensorProductLeftInternalHomCompatibilityMorphism}(list)</span>.</p>

<p><a id="X78BE6DC079995BE8" name="X78BE6DC079995BE8"></a></p>

<h5>1.14-144 AddTensorProductLeftInternalHomCompatibilityMorphismWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddTensorProductLeftInternalHomCompatibilityMorphismWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddTensorProductLeftInternalHomCompatibilityMorphismWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">TensorProductLeftInternalHomCompatibilityMorphismWithGivenObjects</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( source, list, range ) \mapsto \mathtt{TensorProductLeftInternalHomCompatibilityMorphismWithGivenObjects}(source, list, range)</span>.</p>

<p><a id="X7A7B64B17E0CB68F" name="X7A7B64B17E0CB68F"></a></p>

<h5>1.14-145 AddTensorProductToLeftInternalHomAdjunctMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddTensorProductToLeftInternalHomAdjunctMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddTensorProductToLeftInternalHomAdjunctMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">TensorProductToLeftInternalHomAdjunctMorphism</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b, f ) \mapsto \mathtt{TensorProductToLeftInternalHomAdjunctMorphism}(a, b, f)</span>.</p>

<p><a id="X852D330679DA479F" name="X852D330679DA479F"></a></p>

<h5>1.14-146 AddTensorProductToLeftInternalHomAdjunctMorphismWithGivenLeftInternalHom</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddTensorProductToLeftInternalHomAdjunctMorphismWithGivenLeftInternalHom</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddTensorProductToLeftInternalHomAdjunctMorphismWithGivenLeftInternalHom</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">TensorProductToLeftInternalHomAdjunctMorphismWithGivenLeftInternalHom</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b, f, i ) \mapsto \mathtt{TensorProductToLeftInternalHomAdjunctMorphismWithGivenLeftInternalHom}(a, b, f, i)</span>.</p>

<p><a id="X814F44BD7ED47029" name="X814F44BD7ED47029"></a></p>

<h5>1.14-147 AddUniversalPropertyOfLeftDual</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddUniversalPropertyOfLeftDual</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddUniversalPropertyOfLeftDual</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">UniversalPropertyOfLeftDual</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( t, a, alpha ) \mapsto \mathtt{UniversalPropertyOfLeftDual}(t, a, alpha)</span>.</p>

<p><a id="X7DF0FCAF7EF18F8F" name="X7DF0FCAF7EF18F8F"></a></p>

<h5>1.14-148 AddIsomorphismFromLeftCoDualObjectToLeftInternalCoHomFromTensorUnit</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddIsomorphismFromLeftCoDualObjectToLeftInternalCoHomFromTensorUnit</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddIsomorphismFromLeftCoDualObjectToLeftInternalCoHomFromTensorUnit</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">IsomorphismFromLeftCoDualObjectToLeftInternalCoHomFromTensorUnit</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a ) \mapsto \mathtt{IsomorphismFromLeftCoDualObjectToLeftInternalCoHomFromTensorUnit}(a)</span>.</p>

<p><a id="X85BAFAF48192ADFD" name="X85BAFAF48192ADFD"></a></p>

<h5>1.14-149 AddIsomorphismFromLeftInternalCoHomFromTensorUnitToLeftCoDualObject</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddIsomorphismFromLeftInternalCoHomFromTensorUnitToLeftCoDualObject</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddIsomorphismFromLeftInternalCoHomFromTensorUnitToLeftCoDualObject</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">IsomorphismFromLeftInternalCoHomFromTensorUnitToLeftCoDualObject</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a ) \mapsto \mathtt{IsomorphismFromLeftInternalCoHomFromTensorUnitToLeftCoDualObject}(a)</span>.</p>

<p><a id="X7F13CA18790E4170" name="X7F13CA18790E4170"></a></p>

<h5>1.14-150 AddIsomorphismFromLeftInternalCoHomToObject</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddIsomorphismFromLeftInternalCoHomToObject</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddIsomorphismFromLeftInternalCoHomToObject</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">IsomorphismFromLeftInternalCoHomToObject</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a ) \mapsto \mathtt{IsomorphismFromLeftInternalCoHomToObject}(a)</span>.</p>

<p><a id="X8695E6B0854AC59F" name="X8695E6B0854AC59F"></a></p>

<h5>1.14-151 AddIsomorphismFromLeftInternalCoHomToObjectWithGivenLeftInternalCoHom</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddIsomorphismFromLeftInternalCoHomToObjectWithGivenLeftInternalCoHom</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddIsomorphismFromLeftInternalCoHomToObjectWithGivenLeftInternalCoHom</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">IsomorphismFromLeftInternalCoHomToObjectWithGivenLeftInternalCoHom</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, s ) \mapsto \mathtt{IsomorphismFromLeftInternalCoHomToObjectWithGivenLeftInternalCoHom}(a, s)</span>.</p>

<p><a id="X78B4B7FE82DC4548" name="X78B4B7FE82DC4548"></a></p>

<h5>1.14-152 AddIsomorphismFromObjectToLeftInternalCoHom</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddIsomorphismFromObjectToLeftInternalCoHom</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddIsomorphismFromObjectToLeftInternalCoHom</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">IsomorphismFromObjectToLeftInternalCoHom</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a ) \mapsto \mathtt{IsomorphismFromObjectToLeftInternalCoHom}(a)</span>.</p>

<p><a id="X8569A8107E98C1A7" name="X8569A8107E98C1A7"></a></p>

<h5>1.14-153 AddIsomorphismFromObjectToLeftInternalCoHomWithGivenLeftInternalCoHom</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddIsomorphismFromObjectToLeftInternalCoHomWithGivenLeftInternalCoHom</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddIsomorphismFromObjectToLeftInternalCoHomWithGivenLeftInternalCoHom</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">IsomorphismFromObjectToLeftInternalCoHomWithGivenLeftInternalCoHom</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, r ) \mapsto \mathtt{IsomorphismFromObjectToLeftInternalCoHomWithGivenLeftInternalCoHom}(a, r)</span>.</p>

<p><a id="X834FFF597E5AD96E" name="X834FFF597E5AD96E"></a></p>

<h5>1.14-154 AddLeftCoDualOnMorphisms</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftCoDualOnMorphisms</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftCoDualOnMorphisms</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LeftCoDualOnMorphisms</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( alpha ) \mapsto \mathtt{LeftCoDualOnMorphisms}(alpha)</span>.</p>

<p><a id="X7EFAFD687AE8B744" name="X7EFAFD687AE8B744"></a></p>

<h5>1.14-155 AddLeftCoDualOnMorphismsWithGivenLeftCoDuals</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftCoDualOnMorphismsWithGivenLeftCoDuals</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftCoDualOnMorphismsWithGivenLeftCoDuals</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LeftCoDualOnMorphismsWithGivenLeftCoDuals</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( s, alpha, r ) \mapsto \mathtt{LeftCoDualOnMorphismsWithGivenLeftCoDuals}(s, alpha, r)</span>.</p>

<p><a id="X85C97E8D7982AA91" name="X85C97E8D7982AA91"></a></p>

<h5>1.14-156 AddLeftCoDualOnObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftCoDualOnObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftCoDualOnObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LeftCoDualOnObjects</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a ) \mapsto \mathtt{LeftCoDualOnObjects}(a)</span>.</p>

<p><a id="X859C18CA80B931C8" name="X859C18CA80B931C8"></a></p>

<h5>1.14-157 AddLeftCoDualityTensorProductCompatibilityMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftCoDualityTensorProductCompatibilityMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftCoDualityTensorProductCompatibilityMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LeftCoDualityTensorProductCompatibilityMorphism</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b ) \mapsto \mathtt{LeftCoDualityTensorProductCompatibilityMorphism}(a, b)</span>.</p>

<p><a id="X7D8D0BE17F8837FB" name="X7D8D0BE17F8837FB"></a></p>

<h5>1.14-158 AddLeftCoDualityTensorProductCompatibilityMorphismWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftCoDualityTensorProductCompatibilityMorphismWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftCoDualityTensorProductCompatibilityMorphismWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LeftCoDualityTensorProductCompatibilityMorphismWithGivenObjects</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( s, a, b, r ) \mapsto \mathtt{LeftCoDualityTensorProductCompatibilityMorphismWithGivenObjects}(s, a, b, r)</span>.</p>

<p><a id="X788B63417F1F60F9" name="X788B63417F1F60F9"></a></p>

<h5>1.14-159 AddLeftCoclosedMonoidalCoevaluationMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftCoclosedMonoidalCoevaluationMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftCoclosedMonoidalCoevaluationMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LeftCoclosedMonoidalCoevaluationMorphism</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b ) \mapsto \mathtt{LeftCoclosedMonoidalCoevaluationMorphism}(a, b)</span>.</p>

<p><a id="X82B5F67881855573" name="X82B5F67881855573"></a></p>

<h5>1.14-160 AddLeftCoclosedMonoidalCoevaluationMorphismWithGivenSource</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftCoclosedMonoidalCoevaluationMorphismWithGivenSource</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftCoclosedMonoidalCoevaluationMorphismWithGivenSource</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LeftCoclosedMonoidalCoevaluationMorphismWithGivenSource</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b, s ) \mapsto \mathtt{LeftCoclosedMonoidalCoevaluationMorphismWithGivenSource}(a, b, s)</span>.</p>

<p><a id="X7825101881671E7F" name="X7825101881671E7F"></a></p>

<h5>1.14-161 AddLeftCoclosedMonoidalEvaluationForLeftCoDual</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftCoclosedMonoidalEvaluationForLeftCoDual</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftCoclosedMonoidalEvaluationForLeftCoDual</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LeftCoclosedMonoidalEvaluationForLeftCoDual</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a ) \mapsto \mathtt{LeftCoclosedMonoidalEvaluationForLeftCoDual}(a)</span>.</p>

<p><a id="X846EE69A797450F9" name="X846EE69A797450F9"></a></p>

<h5>1.14-162 AddLeftCoclosedMonoidalEvaluationForLeftCoDualWithGivenTensorProduct</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftCoclosedMonoidalEvaluationForLeftCoDualWithGivenTensorProduct</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftCoclosedMonoidalEvaluationForLeftCoDualWithGivenTensorProduct</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LeftCoclosedMonoidalEvaluationForLeftCoDualWithGivenTensorProduct</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( s, a, r ) \mapsto \mathtt{LeftCoclosedMonoidalEvaluationForLeftCoDualWithGivenTensorProduct}(s, a, r)</span>.</p>

<p><a id="X826AE548803450C1" name="X826AE548803450C1"></a></p>

<h5>1.14-163 AddLeftCoclosedMonoidalEvaluationMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftCoclosedMonoidalEvaluationMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftCoclosedMonoidalEvaluationMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LeftCoclosedMonoidalEvaluationMorphism</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b ) \mapsto \mathtt{LeftCoclosedMonoidalEvaluationMorphism}(a, b)</span>.</p>

<p><a id="X8082909C8786B490" name="X8082909C8786B490"></a></p>

<h5>1.14-164 AddLeftCoclosedMonoidalEvaluationMorphismWithGivenRange</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftCoclosedMonoidalEvaluationMorphismWithGivenRange</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftCoclosedMonoidalEvaluationMorphismWithGivenRange</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LeftCoclosedMonoidalEvaluationMorphismWithGivenRange</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b, r ) \mapsto \mathtt{LeftCoclosedMonoidalEvaluationMorphismWithGivenRange}(a, b, r)</span>.</p>

<p><a id="X84635F4580F63BD0" name="X84635F4580F63BD0"></a></p>

<h5>1.14-165 AddLeftCoclosedMonoidalLambdaElimination</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftCoclosedMonoidalLambdaElimination</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftCoclosedMonoidalLambdaElimination</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LeftCoclosedMonoidalLambdaElimination</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b, alpha ) \mapsto \mathtt{LeftCoclosedMonoidalLambdaElimination}(a, b, alpha)</span>.</p>

<p><a id="X83DF33EF7A19E291" name="X83DF33EF7A19E291"></a></p>

<h5>1.14-166 AddLeftCoclosedMonoidalLambdaIntroduction</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftCoclosedMonoidalLambdaIntroduction</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftCoclosedMonoidalLambdaIntroduction</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LeftCoclosedMonoidalLambdaIntroduction</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( alpha ) \mapsto \mathtt{LeftCoclosedMonoidalLambdaIntroduction}(alpha)</span>.</p>

<p><a id="X7954E35E784BCB8B" name="X7954E35E784BCB8B"></a></p>

<h5>1.14-167 AddLeftCoclosedMonoidalPostCoComposeMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftCoclosedMonoidalPostCoComposeMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftCoclosedMonoidalPostCoComposeMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LeftCoclosedMonoidalPostCoComposeMorphism</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b, c ) \mapsto \mathtt{LeftCoclosedMonoidalPostCoComposeMorphism}(a, b, c)</span>.</p>

<p><a id="X7FE2EC92781C752E" name="X7FE2EC92781C752E"></a></p>

<h5>1.14-168 AddLeftCoclosedMonoidalPostCoComposeMorphismWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftCoclosedMonoidalPostCoComposeMorphismWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftCoclosedMonoidalPostCoComposeMorphismWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LeftCoclosedMonoidalPostCoComposeMorphismWithGivenObjects</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( s, a, b, c, r ) \mapsto \mathtt{LeftCoclosedMonoidalPostCoComposeMorphismWithGivenObjects}(s, a, b, c, r)</span>.</p>

<p><a id="X7DC17F0884BAD720" name="X7DC17F0884BAD720"></a></p>

<h5>1.14-169 AddLeftCoclosedMonoidalPreCoComposeMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftCoclosedMonoidalPreCoComposeMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftCoclosedMonoidalPreCoComposeMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LeftCoclosedMonoidalPreCoComposeMorphism</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b, c ) \mapsto \mathtt{LeftCoclosedMonoidalPreCoComposeMorphism}(a, b, c)</span>.</p>

<p><a id="X86DB94FE8301038C" name="X86DB94FE8301038C"></a></p>

<h5>1.14-170 AddLeftCoclosedMonoidalPreCoComposeMorphismWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftCoclosedMonoidalPreCoComposeMorphismWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftCoclosedMonoidalPreCoComposeMorphismWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LeftCoclosedMonoidalPreCoComposeMorphismWithGivenObjects</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( s, a, b, c, r ) \mapsto \mathtt{LeftCoclosedMonoidalPreCoComposeMorphismWithGivenObjects}(s, a, b, c, r)</span>.</p>

<p><a id="X829E5F7E783539C3" name="X829E5F7E783539C3"></a></p>

<h5>1.14-171 AddLeftInternalCoHomOnMorphisms</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftInternalCoHomOnMorphisms</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftInternalCoHomOnMorphisms</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LeftInternalCoHomOnMorphisms</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( alpha, beta ) \mapsto \mathtt{LeftInternalCoHomOnMorphisms}(alpha, beta)</span>.</p>

<p><a id="X78538C8E78635666" name="X78538C8E78635666"></a></p>

<h5>1.14-172 AddLeftInternalCoHomOnMorphismsWithGivenLeftInternalCoHoms</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftInternalCoHomOnMorphismsWithGivenLeftInternalCoHoms</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftInternalCoHomOnMorphismsWithGivenLeftInternalCoHoms</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LeftInternalCoHomOnMorphismsWithGivenLeftInternalCoHoms</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( s, alpha, beta, r ) \mapsto \mathtt{LeftInternalCoHomOnMorphismsWithGivenLeftInternalCoHoms}(s, alpha, beta, r)</span>.</p>

<p><a id="X82901BEB81D0A428" name="X82901BEB81D0A428"></a></p>

<h5>1.14-173 AddLeftInternalCoHomOnObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftInternalCoHomOnObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftInternalCoHomOnObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LeftInternalCoHomOnObjects</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b ) \mapsto \mathtt{LeftInternalCoHomOnObjects}(a, b)</span>.</p>

<p><a id="X814CCC847F369708" name="X814CCC847F369708"></a></p>

<h5>1.14-174 AddLeftInternalCoHomTensorProductCompatibilityMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftInternalCoHomTensorProductCompatibilityMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftInternalCoHomTensorProductCompatibilityMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LeftInternalCoHomTensorProductCompatibilityMorphism</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( list ) \mapsto \mathtt{LeftInternalCoHomTensorProductCompatibilityMorphism}(list)</span>.</p>

<p><a id="X7C3A3DEB7BA72741" name="X7C3A3DEB7BA72741"></a></p>

<h5>1.14-175 AddLeftInternalCoHomTensorProductCompatibilityMorphismWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftInternalCoHomTensorProductCompatibilityMorphismWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftInternalCoHomTensorProductCompatibilityMorphismWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LeftInternalCoHomTensorProductCompatibilityMorphismWithGivenObjects</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( source, list, range ) \mapsto \mathtt{LeftInternalCoHomTensorProductCompatibilityMorphismWithGivenObjects}(source, list, range)</span>.</p>

<p><a id="X80C1A62B812B4565" name="X80C1A62B812B4565"></a></p>

<h5>1.14-176 AddLeftInternalCoHomToTensorProductAdjunctMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftInternalCoHomToTensorProductAdjunctMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftInternalCoHomToTensorProductAdjunctMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LeftInternalCoHomToTensorProductAdjunctMorphism</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, c, f ) \mapsto \mathtt{LeftInternalCoHomToTensorProductAdjunctMorphism}(a, c, f)</span>.</p>

<p><a id="X83DDE598805FFA88" name="X83DDE598805FFA88"></a></p>

<h5>1.14-177 AddLeftInternalCoHomToTensorProductAdjunctMorphismWithGivenTensorProduct</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftInternalCoHomToTensorProductAdjunctMorphismWithGivenTensorProduct</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddLeftInternalCoHomToTensorProductAdjunctMorphismWithGivenTensorProduct</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">LeftInternalCoHomToTensorProductAdjunctMorphismWithGivenTensorProduct</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, c, f, t ) \mapsto \mathtt{LeftInternalCoHomToTensorProductAdjunctMorphismWithGivenTensorProduct}(a, c, f, t)</span>.</p>

<p><a id="X8104426A8327EF5E" name="X8104426A8327EF5E"></a></p>

<h5>1.14-178 AddMorphismFromLeftCoBidual</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddMorphismFromLeftCoBidual</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddMorphismFromLeftCoBidual</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">MorphismFromLeftCoBidual</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a ) \mapsto \mathtt{MorphismFromLeftCoBidual}(a)</span>.</p>

<p><a id="X849C36147F09B8A0" name="X849C36147F09B8A0"></a></p>

<h5>1.14-179 AddMorphismFromLeftCoBidualWithGivenLeftCoBidual</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddMorphismFromLeftCoBidualWithGivenLeftCoBidual</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddMorphismFromLeftCoBidualWithGivenLeftCoBidual</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">MorphismFromLeftCoBidualWithGivenLeftCoBidual</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, s ) \mapsto \mathtt{MorphismFromLeftCoBidualWithGivenLeftCoBidual}(a, s)</span>.</p>

<p><a id="X86168FF07A697A15" name="X86168FF07A697A15"></a></p>

<h5>1.14-180 AddMorphismFromLeftInternalCoHomToTensorProduct</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddMorphismFromLeftInternalCoHomToTensorProduct</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddMorphismFromLeftInternalCoHomToTensorProduct</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">MorphismFromLeftInternalCoHomToTensorProduct</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b ) \mapsto \mathtt{MorphismFromLeftInternalCoHomToTensorProduct}(a, b)</span>.</p>

<p><a id="X830428C27A6BC07B" name="X830428C27A6BC07B"></a></p>

<h5>1.14-181 AddMorphismFromLeftInternalCoHomToTensorProductWithGivenObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddMorphismFromLeftInternalCoHomToTensorProductWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddMorphismFromLeftInternalCoHomToTensorProductWithGivenObjects</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">MorphismFromLeftInternalCoHomToTensorProductWithGivenObjects</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( s, a, b, r ) \mapsto \mathtt{MorphismFromLeftInternalCoHomToTensorProductWithGivenObjects}(s, a, b, r)</span>.</p>

<p><a id="X7AA7EDE881098270" name="X7AA7EDE881098270"></a></p>

<h5>1.14-182 AddTensorProductToLeftInternalCoHomAdjunctMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddTensorProductToLeftInternalCoHomAdjunctMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddTensorProductToLeftInternalCoHomAdjunctMorphism</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">TensorProductToLeftInternalCoHomAdjunctMorphism</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( b, c, g ) \mapsto \mathtt{TensorProductToLeftInternalCoHomAdjunctMorphism}(b, c, g)</span>.</p>

<p><a id="X7CDB23877B3C8292" name="X7CDB23877B3C8292"></a></p>

<h5>1.14-183 AddTensorProductToLeftInternalCoHomAdjunctMorphismWithGivenLeftInternalCoHom</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddTensorProductToLeftInternalCoHomAdjunctMorphismWithGivenLeftInternalCoHom</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddTensorProductToLeftInternalCoHomAdjunctMorphismWithGivenLeftInternalCoHom</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">TensorProductToLeftInternalCoHomAdjunctMorphismWithGivenLeftInternalCoHom</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( b, c, g, i ) \mapsto \mathtt{TensorProductToLeftInternalCoHomAdjunctMorphismWithGivenLeftInternalCoHom}(b, c, g, i)</span>.</p>

<p><a id="X864F1EF47CAD2BE8" name="X864F1EF47CAD2BE8"></a></p>

<h5>1.14-184 AddUniversalPropertyOfLeftCoDual</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddUniversalPropertyOfLeftCoDual</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddUniversalPropertyOfLeftCoDual</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">UniversalPropertyOfLeftCoDual</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( t, a, alpha ) \mapsto \mathtt{UniversalPropertyOfLeftCoDual}(t, a, alpha)</span>.</p>

<p><a id="X79CDE3B87D14EF9A" name="X79CDE3B87D14EF9A"></a></p>

<h5>1.14-185 AddAssociatorLeftToRight</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddAssociatorLeftToRight</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddAssociatorLeftToRight</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">AssociatorLeftToRight</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( a, b, c ) \mapsto \mathtt{AssociatorLeftToRight}(a, b, c)</span>.</p>

<p><a id="X850B5B357F592FAE" name="X850B5B357F592FAE"></a></p>

<h5>1.14-186 AddAssociatorLeftToRightWithGivenTensorProducts</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddAssociatorLeftToRightWithGivenTensorProducts</code>( <var class="Arg">C</var>, <var class="Arg">F</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AddAssociatorLeftToRightWithGivenTensorProducts</code>( <var class="Arg">C</var>, <var class="Arg">F</var>, <var class="Arg">weight</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: nothing</p>

<p>The arguments are a category <span class="Math">C</span> and a function <span class="Math">F</span>. This operation adds the given function <span class="Math">F</span> to the category for the basic operation <code class="code">AssociatorLeftToRightWithGivenTensorProducts</code>. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). <span class="Math">F: ( s, a, b, c, r ) \mapsto \mathtt{AssociatorLeftToRightWithGivenTensorProducts}(s, a, b, c, r)</span>.</p>

<p><a id="X8045C4FC7B4912B4" name="X8045C4FC7B4912B4"></a></p>

<h5>1.14-187 AddAssociatorRightToLeft</h5>

--> --------------------

--> maximum size reached

--> --------------------

Messung V0.5 in Prozent
C=93 H=100 G=96

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