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/a> <a href="chap1_mj.html" >1 </a> <a href="chap2_mj.html" >2 </a> <a href="chap3_mj.html" >3 </a> <a href="chap4_mj.html" >4 </a> <a href="chap5_mj.html" >5 </a> <a href="chap6_mj.html" >6 </a> <a href="chapInd_mj.html" >Ind</a> </div >div class="chlinkprevnexttop" > <a href="chap0_mj.html" >[Top of Book]</a> <a href="chap0_mj.html#contents" >[Contents]</a> <a href="chap1_mj.html" >[Next Chapter]</a> </div >"mathjaxlink" class="pcenter" ><a href="chap0.html" >[MathJax off]</a></p>"X7D2C85EC87DD46E5" name="X7D2C85EC87DD46E5" ></a></p>div class="pcenter" >h1 >MonoidalCategories</h1 >2025 .08 -02 </p>25 August 2025 div >br />Email: <span class="URL" ><a href="mailto:mohamed.barakat@uni-siegen.de" >mohamed.barakat@uni-siegen.de</a></span >br />Homepage: <span class="URL" ><a href="http://algebra.mathematik.uni-siegen.de/barakat/ " >http://algebra.mathematik.uni-siegen.de/barakat/</a></span >br />Address : <br />Walter-Flex-Str. 3 <br /> 57068 Siegen<br /> Germany<br />br />Email: <span class="URL" ><a href="mailto:sebastian.gutsche@gmail.com" >sebastian.gutsche@gmail.com</a></span >br />Homepage: <span class="URL" ><a href="http://algebra.mathematik.uni-siegen.de/gutsche/ " >http://algebra.mathematik.uni-siegen.de/gutsche/</a></span >br />Address : <br />Department Mathematik<br /> Universität Siegen<br /> Walter-Flex-Straße 3 <br /> 57068 Siegen<br /> Germany<br />br />Email: <span class="URL" ><a href="mailto:sebastian.posur@uni-muenster.de" >sebastian.posur@uni-muenster.de</a></span >br />Homepage: <span class="URL" ><a href="http://algebra.mathematik.uni-siegen.de/posur/ " >http://algebra.mathematik.uni-siegen.de/posur/</a></span >br />Address : <br />Department Mathematik<br /> Universität Siegen<br /> Walter-Flex-Straße 3 <br /> 57068 Siegen<br /> Germany<br />br />Email: <span class="URL" ><a href="mailto:tom.kuhmichel@student.uni-siegen.de" >tom.kuhmichel@student.uni-siegen.de</a></span >br />Homepage: <span class="URL" ><a href="https://github.com/TKuh " >https://github.com/TKuh</a></span >br />Address : <br />Department Mathematik<br /> Universität Siegen<br /> Walter-Flex-Straße 3 <br /> 57068 Siegen<br /> Germany<br />br />Email: <span class="URL" ><a href="mailto:f.zickgraf@dashdos.com" >f.zickgraf@dashdos.com</a></span >br />Homepage: <span class="URL" ><a href="https://github.com/zickgraf/ " >https://github.com/zickgraf/</a></span >br />Address : <br />Walter-Flex-Str. 3 <br /> 57068 Siegen<br /> Germany<br />"X8537FEB07AF2BEC8" name="X8537FEB07AF2BEC8" ></a></p>div class="contents" >"contents" name="contents" ></a></h3>div class="ContChap" ><a href="chap1_mj.html#X808DC49C7ED99B52" >1 <span class="Heading" >Monoidal Categories</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap1_mj.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_mj.html#X84997A1E8188D6BE" >1 .1 -1 TensorProductOnMorphisms</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X85008BF07C2C0386" >1 .1 -2 TensorProductOnMorphismsWithGivenTensorProducts</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X84C2FAEA7B9678AA" >1 .1 -3 AssociatorRightToLeft</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X85645C4D86060ED2" >1 .1 -4 AssociatorRightToLeftWithGivenTensorProducts</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7C5A064C7E1995F1" >1 .1 -5 AssociatorLeftToRight</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7C59D73F8389E389" >1 .1 -6 AssociatorLeftToRightWithGivenTensorProducts</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7EBCAFDD81BDB655" >1 .1 -7 LeftUnitor</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7ED284DF7BA21774" >1 .1 -8 LeftUnitorWithGivenTensorProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X79A274078147A9F7" >1 .1 -9 LeftUnitorInverse</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X849609447CAE996B" >1 .1 -10 LeftUnitorInverseWithGivenTensorProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X82F758CB7A23468A" >1 .1 -11 RightUnitor</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X84C8F97F7BF2282D" >1 .1 -12 RightUnitorWithGivenTensorProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X82DC825480E87301" >1 .1 -13 RightUnitorInverse</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X85A8A87C87B33008" >1 .1 -14 RightUnitorInverseWithGivenTensorProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X797034F17AA47EE0" >1 .1 -15 TensorProductOnObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7BF7FFDF8789474A" >1 .1 -16 TensorUnit</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap1_mj.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_mj.html#X7ACF268E7D82B0C9" >1 .2 -1 LeftDistributivityExpanding</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7CA18968862D2285" >1 .2 -2 LeftDistributivityExpandingWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X780322FE7E5A626D" >1 .2 -3 LeftDistributivityFactoring</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X784D8CD685F5F021" >1 .2 -4 LeftDistributivityFactoringWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X8409C74778A4313A" >1 .2 -5 RightDistributivityExpanding</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7DBE629F811DEADC" >1 .2 -6 RightDistributivityExpandingWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X86C5C33786C1DC28" >1 .2 -7 RightDistributivityFactoring</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X795267217F7807CE" >1 .2 -8 RightDistributivityFactoringWithGivenObjects</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap1_mj.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_mj.html#X7C6ADBFE7A8DD1E3" >1 .3 -1 Braiding</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7F4B09A87B2500C0" >1 .3 -2 BraidingWithGivenTensorProducts</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X8195EC5279D3E8D0" >1 .3 -3 BraidingInverse</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X854AFBC67C836769" >1 .3 -4 BraidingInverseWithGivenTensorProducts</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap1_mj.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_mj.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_mj.html#X87A4C0637EB8A18E" >1 .5 -1 LeftInternalHomOnObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X8439FF407D2C9C6E" >1 .5 -2 LeftInternalHomOnMorphisms</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7861C2AD82F62C77" >1 .5 -3 LeftInternalHomOnMorphismsWithGivenLeftInternalHoms</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X82C4FACF83C3611D" >1 .5 -4 LeftClosedMonoidalEvaluationMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X8575A3748713EACF" >1 .5 -5 LeftClosedMonoidalEvaluationMorphismWithGivenSource</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7A526C59812F2A59" >1 .5 -6 LeftClosedMonoidalCoevaluationMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7BC7F1497A00E87A" >1 .5 -7 LeftClosedMonoidalCoevaluationMorphismWithGivenRange</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X83A5A47979C9B92D" >1 .5 -8 TensorProductToLeftInternalHomAdjunctMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7BB734AA7F213B47" >1 .5 -9 TensorProductToLeftInternalHomAdjunctMorphismWithGivenLeftInternalHom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7C7D769879A7DA90" >1 .5 -10 LeftInternalHomToTensorProductAdjunctMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X80431C73861AEC43" >1 .5 -11 LeftInternalHomToTensorProductAdjunctMorphismWithGivenTensorProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X79AC308B847F5177" >1 .5 -12 LeftClosedMonoidalPreComposeMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X78E3E67480AC81F4" >1 .5 -13 LeftClosedMonoidalPreComposeMorphismWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7CFBE32D7F8F16CD" >1 .5 -14 LeftClosedMonoidalPostComposeMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7D5E05257D908A56" >1 .5 -15 LeftClosedMonoidalPostComposeMorphismWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X859959ED7F2CFDCC" >1 .5 -16 LeftDualOnObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7B697FFC7B23A48B" >1 .5 -17 LeftDualOnMorphisms</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X8282E454874316D8" >1 .5 -18 LeftDualOnMorphismsWithGivenLeftDuals</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7FF3227087ABDA8E" >1 .5 -19 LeftClosedMonoidalEvaluationForLeftDual</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X86995E4D7A63E68F" >1 .5 -20 LeftClosedMonoidalEvaluationForLeftDualWithGivenTensorProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X85D2B94A85E3DBD5" >1 .5 -21 MorphismToLeftBidual</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X868774B68189D7E9" >1 .5 -22 MorphismToLeftBidualWithGivenLeftBidual</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7939CEE8854017D2" >1 .5 -23 TensorProductLeftInternalHomCompatibilityMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X798C160A84CA5623" >1 .5 -24 TensorProductLeftInternalHomCompatibilityMorphismWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X8635D47E7835C8AA" >1 .5 -25 TensorProductLeftDualityCompatibilityMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X8435799E83221130" >1 .5 -26 TensorProductLeftDualityCompatibilityMorphismWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X80FE157E81B02827" >1 .5 -27 MorphismFromTensorProductToLeftInternalHom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X78FDDC2986E50825" >1 .5 -28 MorphismFromTensorProductToLeftInternalHomWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7EA425DA848670D9" >1 .5 -29 IsomorphismFromLeftDualObjectToLeftInternalHomIntoTensorUnit</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X781A2D417A8BC8DF" >1 .5 -30 IsomorphismFromLeftInternalHomIntoTensorUnitToLeftDualObject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X82D9D78C7A8DA61A" >1 .5 -31 UniversalPropertyOfLeftDual</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7C7A252A78484873" >1 .5 -32 LeftClosedMonoidalLambdaIntroduction</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X83B3A8FA8363F620" >1 .5 -33 LeftClosedMonoidalLambdaElimination</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7ECAB43778388C41" >1 .5 -34 IsomorphismFromObjectToLeftInternalHom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X874D7D8E81A6AFF1" >1 .5 -35 IsomorphismFromObjectToLeftInternalHomWithGivenLeftInternalHom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7908CF267DDAA38C" >1 .5 -36 IsomorphismFromLeftInternalHomToObject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7B2F235C8444803C" >1 .5 -37 IsomorphismFromLeftInternalHomToObjectWithGivenLeftInternalHom</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap1_mj.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_mj.html#X78AA83E77B380D68" >1 .6 -1 InternalHomOnObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7C0191A483A72F98" >1 .6 -2 InternalHomOnMorphisms</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X861226B47B5CB713" >1 .6 -3 InternalHomOnMorphismsWithGivenInternalHoms</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X844F05DF7DE23F99" >1 .6 -4 ClosedMonoidalRightEvaluationMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X83E6461280B0EB0C" >1 .6 -5 ClosedMonoidalRightEvaluationMorphismWithGivenSource</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7A745E5A836B5E91" >1 .6 -6 ClosedMonoidalRightCoevaluationMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X868AD1A278EBAB03" >1 .6 -7 ClosedMonoidalRightCoevaluationMorphismWithGivenRange</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7BA9C4A184346304" >1 .6 -8 TensorProductToInternalHomRightAdjunctMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X8218B01287CD44E5" >1 .6 -9 TensorProductToInternalHomRightAdjunctMorphismWithGivenInternalHom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X78A16762823E5F1C" >1 .6 -10 TensorProductToInternalHomRightAdjunctionIsomorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X81D37FA282FC8F11" >1 .6 -11 TensorProductToInternalHomRightAdjunctionIsomorphismWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X8271B2767A2DFE76" >1 .6 -12 InternalHomToTensorProductRightAdjunctMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7ACBB0CE7FA4C781" >1 .6 -13 InternalHomToTensorProductRightAdjunctMorphismWithGivenTensorProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X79EEE4757C27C26E" >1 .6 -14 InternalHomToTensorProductRightAdjunctionIsomorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7B4CD74A7CE51263" >1 .6 -15 InternalHomToTensorProductRightAdjunctionIsomorphismWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X80B3C53A854B515B" >1 .6 -16 ClosedMonoidalLeftEvaluationMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X84E1E136819BDA89" >1 .6 -17 ClosedMonoidalLeftEvaluationMorphismWithGivenSource</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7E35DEB787A71A1F" >1 .6 -18 ClosedMonoidalLeftCoevaluationMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X8196CE5D7C88D83C" >1 .6 -19 ClosedMonoidalLeftCoevaluationMorphismWithGivenRange</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X80A58B1F80A186BD" >1 .6 -20 TensorProductToInternalHomLeftAdjunctMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7CCE373482D60A57" >1 .6 -21 TensorProductToInternalHomLeftAdjunctMorphismWithGivenInternalHom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X793BAA50819573E4" >1 .6 -22 TensorProductToInternalHomLeftAdjunctionIsomorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X791276987824CDF8" >1 .6 -23 TensorProductToInternalHomLeftAdjunctionIsomorphismWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X85F426677EB81BCF" >1 .6 -24 InternalHomToTensorProductLeftAdjunctMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X859B738881052D1C" >1 .6 -25 InternalHomToTensorProductLeftAdjunctMorphismWithGivenTensorProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X86AD79F17F8CEE96" >1 .6 -26 InternalHomToTensorProductLeftAdjunctionIsomorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7D707B26863D508A" >1 .6 -27 InternalHomToTensorProductLeftAdjunctionIsomorphismWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X86E4E97C82BFB45C" >1 .6 -28 MonoidalPreComposeMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7FE4A52284060F20" >1 .6 -29 MonoidalPreComposeMorphismWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X79F4FCE781385829" >1 .6 -30 MonoidalPostComposeMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7E6933B8816EE4E3" >1 .6 -31 MonoidalPostComposeMorphismWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X80FFC71D7E57DD53" >1 .6 -32 DualOnObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X815C0BC47D000819" >1 .6 -33 DualOnMorphisms</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7DCC0F468386AA46" >1 .6 -34 DualOnMorphismsWithGivenDuals</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X86D42C7587F03A68" >1 .6 -35 EvaluationForDual</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7B588B1B8472834E" >1 .6 -36 EvaluationForDualWithGivenTensorProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7F68B55781C1DFB1" >1 .6 -37 MorphismToBidual</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X79260E5680F1E741" >1 .6 -38 MorphismToBidualWithGivenBidual</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X80CDA0CB821E08EE" >1 .6 -39 TensorProductInternalHomCompatibilityMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7B0194A07AB73486" >1 .6 -40 TensorProductInternalHomCompatibilityMorphismWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7D173DB08132E40A" >1 .6 -41 TensorProductDualityCompatibilityMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X794ED97782B8DF76" >1 .6 -42 TensorProductDualityCompatibilityMorphismWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X8439BFF57BFE390F" >1 .6 -43 MorphismFromTensorProductToInternalHom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X8473D28B7F3A5E20" >1 .6 -44 MorphismFromTensorProductToInternalHomWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X8430726C82D6CFF7" >1 .6 -45 IsomorphismFromDualObjectToInternalHomIntoTensorUnit</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7A015736812A97C6" >1 .6 -46 IsomorphismFromInternalHomIntoTensorUnitToDualObject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7AF8F68887146C20" >1 .6 -47 UniversalPropertyOfDual</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X80F3F2287B9E55E3" >1 .6 -48 LambdaIntroduction</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X79EC44077F661E80" >1 .6 -49 LambdaElimination</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X8726BA888787D53D" >1 .6 -50 IsomorphismFromObjectToInternalHom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X87F91EF37C76A7F7" >1 .6 -51 IsomorphismFromObjectToInternalHomWithGivenInternalHom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X831CF4E1824FA178" >1 .6 -52 IsomorphismFromInternalHomToObject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7988DC7C79BED3B2" >1 .6 -53 IsomorphismFromInternalHomToObjectWithGivenInternalHom</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap1_mj.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_mj.html#X7CE5D10B7F10E9CC" >1 .7 -1 LeftInternalCoHomOnObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X853213767BB48099" >1 .7 -2 LeftInternalCoHomOnMorphisms</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7F302E3880752A2F" >1 .7 -3 LeftInternalCoHomOnMorphismsWithGivenLeftInternalCoHoms</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X819A762D83B1C294" >1 .7 -4 LeftCoclosedMonoidalEvaluationMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7E5607B1789E00B7" >1 .7 -5 LeftCoclosedMonoidalEvaluationMorphismWithGivenRange</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X81A249CE84828A9D" >1 .7 -6 LeftCoclosedMonoidalCoevaluationMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7D1018A284F21140" >1 .7 -7 LeftCoclosedMonoidalCoevaluationMorphismWithGivenSource</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X851216B2807B3900" >1 .7 -8 TensorProductToLeftInternalCoHomAdjunctMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X87BFA0FA7AFF2868" >1 .7 -9 TensorProductToLeftInternalCoHomAdjunctMorphismWithGivenLeftInternalCoHom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7DDDACD58454C3A4" >1 .7 -10 LeftInternalCoHomToTensorProductAdjunctMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X821AC96981CA794C" >1 .7 -11 LeftInternalCoHomToTensorProductAdjunctMorphismWithGivenTensorProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X8416357982DCBEE4" >1 .7 -12 LeftCoclosedMonoidalPreCoComposeMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7EECDE4583E14A59" >1 .7 -13 LeftCoclosedMonoidalPreCoComposeMorphismWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X80A270E982F5BC2D" >1 .7 -14 LeftCoclosedMonoidalPostCoComposeMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X867C6F087D72AB3F" >1 .7 -15 LeftCoclosedMonoidalPostCoComposeMorphismWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X85A63AA57F0678EE" >1 .7 -16 LeftCoDualOnObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7949DE307D2D5083" >1 .7 -17 LeftCoDualOnMorphisms</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X84C835CB7E708596" >1 .7 -18 LeftCoDualOnMorphismsWithGivenLeftCoDuals</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7A20AC6A837F79BA" >1 .7 -19 LeftCoclosedMonoidalEvaluationForLeftCoDual</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X87B15AC678955783" >1 .7 -20 LeftCoclosedMonoidalEvaluationForLeftCoDualWithGivenTensorProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7F67676A85A47BDB" >1 .7 -21 MorphismFromLeftCoBidual</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7AF5F77180E09AAE" >1 .7 -22 MorphismFromLeftCoBidualWithGivenLeftCoBidual</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X84331A1B7F62782F" >1 .7 -23 LeftInternalCoHomTensorProductCompatibilityMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X808BEB0879D58CAF" >1 .7 -24 LeftInternalCoHomTensorProductCompatibilityMorphismWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7B4A66A8803C99BA" >1 .7 -25 LeftCoDualityTensorProductCompatibilityMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X86E72092788A8F2D" >1 .7 -26 LeftCoDualityTensorProductCompatibilityMorphismWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7A5FDE4B83C5F328" >1 .7 -27 MorphismFromLeftInternalCoHomToTensorProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7BD2A33F84A2FBAB" >1 .7 -28 MorphismFromLeftInternalCoHomToTensorProductWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7CC10C9E7EA7EED4" >1 .7 -29 IsomorphismFromLeftCoDualObjectToLeftInternalCoHomFromTensorUnit</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X87F96B047F320A17" >1 .7 -30 IsomorphismFromLeftInternalCoHomFromTensorUnitToLeftCoDualObject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7A0DE1667FF28457" >1 .7 -31 UniversalPropertyOfLeftCoDual</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X85960F7479FFA8DA" >1 .7 -32 LeftCoclosedMonoidalLambdaIntroduction</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X8721DDEC7DF9D89D" >1 .7 -33 LeftCoclosedMonoidalLambdaElimination</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X853342457CC3B489" >1 .7 -34 IsomorphismFromObjectToLeftInternalCoHom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X82709BED807CB6FC" >1 .7 -35 IsomorphismFromObjectToLeftInternalCoHomWithGivenLeftInternalCoHom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X806C843B82108148" >1 .7 -36 IsomorphismFromLeftInternalCoHomToObject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X8370164B7EAF833D" >1 .7 -37 IsomorphismFromLeftInternalCoHomToObjectWithGivenLeftInternalCoHom</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap1_mj.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_mj.html#X791BE0B0847A430D" >1 .8 -1 InternalCoHomOnObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7FDF105D7F56EB53" >1 .8 -2 InternalCoHomOnMorphisms</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X84DDA3DD878162B9" >1 .8 -3 InternalCoHomOnMorphismsWithGivenInternalCoHoms</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X83CEC88D79AE5684" >1 .8 -4 CoclosedMonoidalRightEvaluationMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X79333EC9822EA316" >1 .8 -5 CoclosedMonoidalRightEvaluationMorphismWithGivenRange</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X80CA11547F3909E3" >1 .8 -6 CoclosedMonoidalRightCoevaluationMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7F1C10897EC4D14E" >1 .8 -7 CoclosedMonoidalRightCoevaluationMorphismWithGivenSource</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X82B0937678F04730" >1 .8 -8 TensorProductToInternalCoHomRightAdjunctMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X833D7B567810D7F3" >1 .8 -9 TensorProductToInternalCoHomRightAdjunctMorphismWithGivenInternalCoHom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X8623CC567D687FFD" >1 .8 -10 InternalCoHomToTensorProductRightAdjunctMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X821B5212835BD1F6" >1 .8 -11 InternalCoHomToTensorProductRightAdjunctMorphismWithGivenTensorProduct</a></span span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X81020D9E85C3280A" >1 .8 -12 CoclosedMonoidalLeftEvaluationMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7A1801D77EECEA29" >1 .8 -13 CoclosedMonoidalLeftEvaluationMorphismWithGivenRange</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7D6905F582F06003" >1 .8 -14 CoclosedMonoidalLeftCoevaluationMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X802A3FC48280FBDE" >1 .8 -15 CoclosedMonoidalLeftCoevaluationMorphismWithGivenSource</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7FB4953B7F813D0B" >1 .8 -16 TensorProductToInternalCoHomLeftAdjunctMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X8312DB0A82A97D4B" >1 .8 -17 TensorProductToInternalCoHomLeftAdjunctMorphismWithGivenInternalCoHom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7A7FC1957A1905C6" >1 .8 -18 InternalCoHomToTensorProductLeftAdjunctMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X85F970897F87BF2E" >1 .8 -19 InternalCoHomToTensorProductLeftAdjunctMorphismWithGivenTensorProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X8337DE6B7D61EAC2" >1 .8 -20 MonoidalPreCoComposeMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X82A183B0807A0A01" >1 .8 -21 MonoidalPreCoComposeMorphismWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X83FE0B8D853A76C1" >1 .8 -22 MonoidalPostCoComposeMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X805DF38880B1E9E0" >1 .8 -23 MonoidalPostCoComposeMorphismWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X817A1F7986256461" >1 .8 -24 CoDualOnObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X840CBC837926138E" >1 .8 -25 CoDualOnMorphisms</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X79750BFD824D2AAF" >1 .8 -26 CoDualOnMorphismsWithGivenCoDuals</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7C65C05A788415E4" >1 .8 -27 CoclosedEvaluationForCoDual</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7CAB615C86D97CE8" >1 .8 -28 CoclosedEvaluationForCoDualWithGivenTensorProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7841B6757A510799" >1 .8 -29 MorphismFromCoBidual</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7B2B002979E1CBF6" >1 .8 -30 MorphismFromCoBidualWithGivenCoBidual</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7D9E57197C820E0E" >1 .8 -31 InternalCoHomTensorProductCompatibilityMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X81E9DC8D7FCD361F" >1 .8 -32 InternalCoHomTensorProductCompatibilityMorphismWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7B817BC97C1F1DF8" >1 .8 -33 CoDualityTensorProductCompatibilityMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X82119ED686D3874C" >1 .8 -34 CoDualityTensorProductCompatibilityMorphismWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7A4971267B80B14F" >1 .8 -35 MorphismFromInternalCoHomToTensorProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7B60FB927C37E125" >1 .8 -36 MorphismFromInternalCoHomToTensorProductWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X86C7E40C85318EFA" >1 .8 -37 IsomorphismFromCoDualObjectToInternalCoHomFromTensorUnit</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X84C86E29800BB8BC" >1 .8 -38 IsomorphismFromInternalCoHomFromTensorUnitToCoDualObject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7AEE412D80799D09" >1 .8 -39 UniversalPropertyOfCoDual</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X784CBFB984E66E7A" >1 .8 -40 CoLambdaIntroduction</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X83520B098068CF62" >1 .8 -41 CoLambdaElimination</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X83F11F6184DBD507" >1 .8 -42 IsomorphismFromObjectToInternalCoHom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X8233C995828387E9" >1 .8 -43 IsomorphismFromObjectToInternalCoHomWithGivenInternalCoHom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X875A349280E2095C" >1 .8 -44 IsomorphismFromInternalCoHomToObject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X858AD1F986BA5BB2" >1 .8 -45 IsomorphismFromInternalCoHomToObjectWithGivenInternalCoHom</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap1_mj.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_mj.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_mj.html#X805AEF9784062A31" >1 .11 <span class="Heading" >Rigid Symmetric Closed Monoidal Categories</span span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X782B629D7E7835C9" >1 .11 -1 IsomorphismFromTensorProductWithDualObjectToInternalHom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X84D0668C7CA0B63D" >1 .11 -2 IsomorphismFromInternalHomToTensorProductWithDualObject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7D189B8280CECBA2" >1 .11 -3 MorphismFromInternalHomToTensorProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7D10805D840AAC8D" >1 .11 -4 MorphismFromInternalHomToTensorProductWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X85BA8C10817296F7" >1 .11 -5 TensorProductInternalHomCompatibilityMorphismInverse</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7CCE67B281EF45C1" >1 .11 -6 TensorProductInternalHomCompatibilityMorphismInverseWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X83849B327C8074E9" >1 .11 -7 CoevaluationForDual</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7C65E6A97AAE0DE3" >1 .11 -8 CoevaluationForDualWithGivenTensorProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X85D0C9487A22AFFE" >1 .11 -9 TraceMap</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X82F0DBD485D93793" >1 .11 -10 RankMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7E02E8197EA201EA" >1 .11 -11 MorphismFromBidual</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X785CF0BB7BC0AC0D" >1 .11 -12 MorphismFromBidualWithGivenBidual</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap1_mj.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_mj.html#X82D4EF587F1C194C" >1 .12 -1 IsomorphismFromInternalCoHomToTensorProductWithCoDualObject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7FE736BA834D228A" >1 .12 -2 IsomorphismFromTensorProductWithCoDualObjectToInternalCoHom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7DCA54857A6B45DF" >1 .12 -3 MorphismFromTensorProductToInternalCoHom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7888F9947DDC15B5" >1 .12 -4 MorphismFromTensorProductToInternalCoHomWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7E71AF0985C5AEC5" >1 .12 -5 InternalCoHomTensorProductCompatibilityMorphismInverse</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X87BF8BE67AD5ABCF" >1 .12 -6 InternalCoHomTensorProductCompatibilityMorphismInverseWithGivenObjects</a></span span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X8695F9D97A8C6C61" >1 .12 -7 CoclosedCoevaluationForCoDual</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X78B2703A7B81E340" >1 .12 -8 CoclosedCoevaluationForCoDualWithGivenTensorProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X829BE5F97A656200" >1 .12 -9 CoTraceMap</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7C5CC8F97D95AD43" >1 .12 -10 CoRankMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X85BDB94D85C67725" >1 .12 -11 MorphismToCoBidual</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X800035BF867418D0" >1 .12 -12 MorphismToCoBidualWithGivenCoBidual</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap1_mj.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_mj.html#X8055FF847AC2102A" >1 .13 -1 InternalHom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7CB6A9497A971F59" >1 .13 -2 InternalCoHom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X82DE5FDA794914A0" >1 .13 -3 LeftInternalHom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X862E6A787C9E1F92" >1 .13 -4 LeftInternalCoHom</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap1_mj.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_mj.html#X78DA7EC37A1E0CCC" >1 .14 -1 AddLeftDistributivityExpanding</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X814BA200802D26E4" >1 .14 -2 AddLeftDistributivityExpandingWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X8381C23A8264435B" >1 .14 -3 AddLeftDistributivityFactoring</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7F0A439478576973" >1 .14 -4 AddLeftDistributivityFactoringWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X82E93F8E79CB7338" >1 .14 -5 AddRightDistributivityExpanding</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7A6178C17EFC817A" >1 .14 -6 AddRightDistributivityExpandingWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X79B283777BC5F12C" >1 .14 -7 AddRightDistributivityFactoring</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X842099557CF2036E" >1 .14 -8 AddRightDistributivityFactoringWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7F9C3FD38397D9D4" >1 .14 -9 AddBraiding</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X8423AA1A862E9780" >1 .14 -10 AddBraidingInverse</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X85C7E40583A5955F" >1 .14 -11 AddBraidingInverseWithGivenTensorProducts</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7A52CBE8801D6B28" >1 .14 -12 AddBraidingWithGivenTensorProducts</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7996A3A980BD5783" >1 .14 -13 AddClosedMonoidalLeftCoevaluationMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7FD9DC1D870FB3D2" >1 .14 -14 AddClosedMonoidalLeftCoevaluationMorphismWithGivenRange</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X82E0E46E7B374DA9" >1 .14 -15 AddClosedMonoidalLeftEvaluationMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X8742C27B7D30E543" >1 .14 -16 AddClosedMonoidalLeftEvaluationMorphismWithGivenSource</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X870332B286200F2A" >1 .14 -17 AddClosedMonoidalRightCoevaluationMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7A06D2CC79874E18" >1 .14 -18 AddClosedMonoidalRightCoevaluationMorphismWithGivenRange</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X82FD88E87B30334F" >1 .14 -19 AddClosedMonoidalRightEvaluationMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7ECDA3E47F267341" >1 .14 -20 AddClosedMonoidalRightEvaluationMorphismWithGivenSource</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X800DFCF37CC10CCC" >1 .14 -21 AddDualOnMorphisms</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X85DA12C581E673DE" >1 .14 -22 AddDualOnMorphismsWithGivenDuals</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7BB4DD5381EBF082" >1 .14 -23 AddDualOnObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7FF9C96186646B7C" >1 .14 -24 AddEvaluationForDual</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7CB63A4E7E905CD4" >1 .14 -25 AddEvaluationForDualWithGivenTensorProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X79A5E1EF7F091948" >1 .14 -26 AddInternalHomOnMorphisms</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X8070203E80388349" >1 .14 -27 AddInternalHomOnMorphismsWithGivenInternalHoms</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7B74F8FD8348D590" >1 .14 -28 AddInternalHomOnObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X87D40CEF8247DF33" >1 .14 -29 AddInternalHomToTensorProductLeftAdjunctMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X82D3E7BD7DD67116" >1 .14 -30 AddInternalHomToTensorProductLeftAdjunctMorphismWithGivenTensorProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7BBC91088476613F" >1 .14 -31 AddInternalHomToTensorProductLeftAdjunctionIsomorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X789D0ED680E7D176" >1 .14 -32 AddInternalHomToTensorProductLeftAdjunctionIsomorphismWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X84B3BDBF8294E790" >1 .14 -33 AddInternalHomToTensorProductRightAdjunctMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X807104E57D50EEB9" >1 .14 -34 AddInternalHomToTensorProductRightAdjunctMorphismWithGivenTensorProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X8634234A855F18D5" >1 .14 -35 AddInternalHomToTensorProductRightAdjunctionIsomorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7A3FED8E84CD4A02" >1 .14 -36 AddInternalHomToTensorProductRightAdjunctionIsomorphismWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7983CB57783E6813" >1 .14 -37 AddIsomorphismFromDualObjectToInternalHomIntoTensorUnit</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X84E4949886CB84C9" >1 .14 -38 AddIsomorphismFromInternalHomIntoTensorUnitToDualObject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7FA9FE2B85CE866D" >1 .14 -39 AddIsomorphismFromInternalHomToObject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7D6421147BF6651B" >1 .14 -40 AddIsomorphismFromInternalHomToObjectWithGivenInternalHom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X82538F687DE872DD" >1 .14 -41 AddIsomorphismFromObjectToInternalHom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X78ED7FCC83D091AB" >1 .14 -42 AddIsomorphismFromObjectToInternalHomWithGivenInternalHom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X8406FBCD7EE968FF" >1 .14 -43 AddLambdaElimination</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X84944B6283F2802A" >1 .14 -44 AddLambdaIntroduction</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X843DC64486CB2ED1" >1 .14 -45 AddMonoidalPostComposeMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7FC3725A7CF804F9" >1 .14 -46 AddMonoidalPostComposeMorphismWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7B0C198782C01CBA" >1 .14 -47 AddMonoidalPreComposeMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7A22CD657A2A338C" >1 .14 -48 AddMonoidalPreComposeMorphismWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7CF664D87D8D5CA1" >1 .14 -49 AddMorphismFromTensorProductToInternalHom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X86D3AF4A80FA738D" >1 .14 -50 AddMorphismFromTensorProductToInternalHomWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X864B98B08041EE6C" >1 .14 -51 AddMorphismToBidual</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X84C05B087EFCE599" >1 .14 -52 AddMorphismToBidualWithGivenBidual</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7A020DBF860317F5" >1 .14 -53 AddTensorProductDualityCompatibilityMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X78D1B6AF8654A950" >1 .14 -54 AddTensorProductDualityCompatibilityMorphismWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X83A6EF0B7ED71EED" >1 .14 -55 AddTensorProductInternalHomCompatibilityMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X871C6B55843A0AF3" >1 .14 -56 AddTensorProductInternalHomCompatibilityMorphismWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X817EAD878544BF68" >1 .14 -57 AddTensorProductToInternalHomLeftAdjunctMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7B2FEF0985C2FACE" >1 .14 -58 AddTensorProductToInternalHomLeftAdjunctMorphismWithGivenInternalHom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X85A8D11983750164" >1 .14 -59 AddTensorProductToInternalHomLeftAdjunctionIsomorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7AE873FD87E4B12D" >1 .14 -60 AddTensorProductToInternalHomLeftAdjunctionIsomorphismWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7AF5FBEE859787CB" >1 .14 -61 AddTensorProductToInternalHomRightAdjunctMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X86B3F2BF813AFBDA" >1 .14 -62 AddTensorProductToInternalHomRightAdjunctMorphismWithGivenInternalHom</a></span span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X79777C5F825C788E" >1 .14 -63 AddTensorProductToInternalHomRightAdjunctionIsomorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X86FD5F8A83CE2A59" >1 .14 -64 AddTensorProductToInternalHomRightAdjunctionIsomorphismWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7FCEDB3B7DF69A1E" >1 .14 -65 AddUniversalPropertyOfDual</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7D23088385F021AA" >1 .14 -66 AddCoDualOnMorphisms</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7C2568FD82259231" >1 .14 -67 AddCoDualOnMorphismsWithGivenCoDuals</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7C1CDE7F855ACB74" >1 .14 -68 AddCoDualOnObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7D9B355D8261CB17" >1 .14 -69 AddCoDualityTensorProductCompatibilityMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7CE8010980DBA597" >1 .14 -70 AddCoDualityTensorProductCompatibilityMorphismWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7E7962CC7E809023" >1 .14 -71 AddCoLambdaElimination</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7C3868657D8A0400" >1 .14 -72 AddCoLambdaIntroduction</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X839204FD79F2968D" >1 .14 -73 AddCoclosedEvaluationForCoDual</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X803976DB7C8F307C" >1 .14 -74 AddCoclosedEvaluationForCoDualWithGivenTensorProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X829CAF887FAC5BF0" >1 .14 -75 AddCoclosedMonoidalLeftCoevaluationMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7E7EBA4381366E7A" >1 .14 -76 AddCoclosedMonoidalLeftCoevaluationMorphismWithGivenSource</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X81EC6B3E80876BC8" >1 .14 -77 AddCoclosedMonoidalLeftEvaluationMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X839DE15C87358F99" >1 .14 -78 AddCoclosedMonoidalLeftEvaluationMorphismWithGivenRange</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X78A8CB687ADC4653" >1 .14 -79 AddCoclosedMonoidalRightCoevaluationMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X783C75CD79B2E8C9" >1 .14 -80 AddCoclosedMonoidalRightCoevaluationMorphismWithGivenSource</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X85F82B2F84E55DD2" >1 .14 -81 AddCoclosedMonoidalRightEvaluationMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X86DC2EF07B421CE0" >1 .14 -82 AddCoclosedMonoidalRightEvaluationMorphismWithGivenRange</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7D63C4A57A467DAA" >1 .14 -83 AddInternalCoHomOnMorphisms</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X87A67CDD86E0CE05" >1 .14 -84 AddInternalCoHomOnMorphismsWithGivenInternalCoHoms</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X828648F183570AE3" >1 .14 -85 AddInternalCoHomOnObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X78278696834ACA53" >1 .14 -86 AddInternalCoHomTensorProductCompatibilityMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X82EA4C857C7BCC60" >1 .14 -87 AddInternalCoHomTensorProductCompatibilityMorphismWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7C7256EE79374540" >1 .14 -88 AddInternalCoHomToTensorProductLeftAdjunctMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X84EBD01D7843FAAD" >1 .14 -89 AddInternalCoHomToTensorProductLeftAdjunctMorphismWithGivenTensorProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X858ED26087369677" >1 .14 -90 AddInternalCoHomToTensorProductRightAdjunctMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7E97DAC0782AACEC" >1 .14 -91 AddInternalCoHomToTensorProductRightAdjunctMorphismWithGivenTensorProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7A2B14497B4924A7" >1 .14 -92 AddIsomorphismFromCoDualObjectToInternalCoHomFromTensorUnit</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X8143326C7BE5E321" >1 .14 -93 AddIsomorphismFromInternalCoHomFromTensorUnitToCoDualObject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7C9F35A779395B26" >1 .14 -94 AddIsomorphismFromInternalCoHomToObject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7D0E88AC7C0304D3" >1 .14 -95 AddIsomorphismFromInternalCoHomToObjectWithGivenInternalCoHom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7E18F31C86620139" >1 .14 -96 AddIsomorphismFromObjectToInternalCoHom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X8304276383585ECC" >1 .14 -97 AddIsomorphismFromObjectToInternalCoHomWithGivenInternalCoHom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7DE479077F155716" >1 .14 -98 AddMonoidalPostCoComposeMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X79858B577BD4F1E1" >1 .14 -99 AddMonoidalPostCoComposeMorphismWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7D1662EA819EA1A2" >1 .14 -100 AddMonoidalPreCoComposeMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X81DFED7386A953E0" >1 .14 -101 AddMonoidalPreCoComposeMorphismWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7D1615257BAA311F" >1 .14 -102 AddMorphismFromCoBidual</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X84D1F74D8118B2A0" >1 .14 -103 AddMorphismFromCoBidualWithGivenCoBidual</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7C3C01F1834A4B9B" >1 .14 -104 AddMorphismFromInternalCoHomToTensorProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X87AB2C4D84F19F37" >1 .14 -105 AddMorphismFromInternalCoHomToTensorProductWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7C0E0CF87FEFEB0D" >1 .14 -106 AddTensorProductToInternalCoHomLeftAdjunctMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7A838651781657DA" >1 .14 -107 AddTensorProductToInternalCoHomLeftAdjunctMorphismWithGivenInternalCoHom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X8123546E81EE383A" >1 .14 -108 AddTensorProductToInternalCoHomRightAdjunctMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X8698898584E99695" >1 .14 -109 AddTensorProductToInternalCoHomRightAdjunctMorphismWithGivenInternalCoHom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X8519ECF17EC07916" >1 .14 -110 AddUniversalPropertyOfCoDual</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7F868E597F1C1AD7" >1 .14 -111 AddIsomorphismFromLeftDualObjectToLeftInternalHomIntoTensorUnit</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X810B50C27901021C" >1 .14 -112 AddIsomorphismFromLeftInternalHomIntoTensorUnitToLeftDualObject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X87415032853E8340" >1 .14 -113 AddIsomorphismFromLeftInternalHomToObject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X83DAADEE8139DACA" >1 .14 -114 AddIsomorphismFromLeftInternalHomToObjectWithGivenLeftInternalHom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7FA337D07BCD9D5B" >1 .14 -115 AddIsomorphismFromObjectToLeftInternalHom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7EA7B1777FCAC4D1" >1 .14 -116 AddIsomorphismFromObjectToLeftInternalHomWithGivenLeftInternalHom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7D1E4F66851991AB" >1 .14 -117 AddLeftClosedMonoidalCoevaluationMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7EF0D5B782AB75FA" >1 .14 -118 AddLeftClosedMonoidalCoevaluationMorphismWithGivenRange</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7FD8142C7CBF7FB1" >1 .14 -119 AddLeftClosedMonoidalEvaluationForLeftDual</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7A89130185CCF31D" >1 .14 -120 AddLeftClosedMonoidalEvaluationForLeftDualWithGivenTensorProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7D75530C7E938B81" >1 .14 -121 AddLeftClosedMonoidalEvaluationMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X8535FD8E7894236B" >1 .14 -122 AddLeftClosedMonoidalEvaluationMorphismWithGivenSource</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X869B3FD87FC09E21" >1 .14 -123 AddLeftClosedMonoidalLambdaElimination</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7CC085AB7DBC581A" >1 .14 -124 AddLeftClosedMonoidalLambdaIntroduction</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7BE971CB7E989544" >1 .14 -125 AddLeftClosedMonoidalPostComposeMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7B6DBF17796A971A" >1 .14 -126 AddLeftClosedMonoidalPostComposeMorphismWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X799401467830D201" >1 .14 -127 AddLeftClosedMonoidalPreComposeMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7915D4437C9257A5" >1 .14 -128 AddLeftClosedMonoidalPreComposeMorphismWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X79D85C017917C1D4" >1 .14 -129 AddLeftDualOnMorphisms</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X816C625A82BCDDE3" >1 .14 -130 AddLeftDualOnMorphismsWithGivenLeftDuals</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7CB93B6E8555359D" >1 .14 -131 AddLeftDualOnObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X79B3B2F586530EFF" >1 .14 -132 AddLeftInternalHomOnMorphisms</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7DDC722B78B659A2" >1 .14 -133 AddLeftInternalHomOnMorphismsWithGivenLeftInternalHoms</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7FCF9DEA7F6B73F9" >1 .14 -134 AddLeftInternalHomOnObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7F5EAC1E8104166E" >1 .14 -135 AddLeftInternalHomToTensorProductAdjunctMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7C437ED77E95B84B" >1 .14 -136 AddLeftInternalHomToTensorProductAdjunctMorphismWithGivenTensorProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7CA082FF7B01D8FB" >1 .14 -137 AddMorphismFromTensorProductToLeftInternalHom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X8028DDA77A2AF1D0" >1 .14 -138 AddMorphismFromTensorProductToLeftInternalHomWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X80EC71197C2C11D1" >1 .14 -139 AddMorphismToLeftBidual</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X869265BC78942371" >1 .14 -140 AddMorphismToLeftBidualWithGivenLeftBidual</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7953DC1F805D8C1A" >1 .14 -141 AddTensorProductLeftDualityCompatibilityMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X836F9F347AB09804" >1 .14 -142 AddTensorProductLeftDualityCompatibilityMorphismWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7A76B21F7DD29DD4" >1 .14 -143 AddTensorProductLeftInternalHomCompatibilityMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X78BE6DC079995BE8" >1 .14 -144 AddTensorProductLeftInternalHomCompatibilityMorphismWithGivenObjects</a></span span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7A7B64B17E0CB68F" >1 .14 -145 AddTensorProductToLeftInternalHomAdjunctMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X852D330679DA479F" >1 .14 -146 AddTensorProductToLeftInternalHomAdjunctMorphismWithGivenLeftInternalHom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X814F44BD7ED47029" >1 .14 -147 AddUniversalPropertyOfLeftDual</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7DF0FCAF7EF18F8F" >1 .14 -148 AddIsomorphismFromLeftCoDualObjectToLeftInternalCoHomFromTensorUnit</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X85BAFAF48192ADFD" >1 .14 -149 AddIsomorphismFromLeftInternalCoHomFromTensorUnitToLeftCoDualObject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7F13CA18790E4170" >1 .14 -150 AddIsomorphismFromLeftInternalCoHomToObject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X8695E6B0854AC59F" >1 .14 -151 AddIsomorphismFromLeftInternalCoHomToObjectWithGivenLeftInternalCoHom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X78B4B7FE82DC4548" >1 .14 -152 AddIsomorphismFromObjectToLeftInternalCoHom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X8569A8107E98C1A7" >1 .14 -153 AddIsomorphismFromObjectToLeftInternalCoHomWithGivenLeftInternalCoHom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X834FFF597E5AD96E" >1 .14 -154 AddLeftCoDualOnMorphisms</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7EFAFD687AE8B744" >1 .14 -155 AddLeftCoDualOnMorphismsWithGivenLeftCoDuals</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X85C97E8D7982AA91" >1 .14 -156 AddLeftCoDualOnObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X859C18CA80B931C8" >1 .14 -157 AddLeftCoDualityTensorProductCompatibilityMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7D8D0BE17F8837FB" >1 .14 -158 AddLeftCoDualityTensorProductCompatibilityMorphismWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X788B63417F1F60F9" >1 .14 -159 AddLeftCoclosedMonoidalCoevaluationMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X82B5F67881855573" >1 .14 -160 AddLeftCoclosedMonoidalCoevaluationMorphismWithGivenSource</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7825101881671E7F" >1 .14 -161 AddLeftCoclosedMonoidalEvaluationForLeftCoDual</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X846EE69A797450F9" >1 .14 -162 AddLeftCoclosedMonoidalEvaluationForLeftCoDualWithGivenTensorProduct</a></span span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X826AE548803450C1" >1 .14 -163 AddLeftCoclosedMonoidalEvaluationMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X8082909C8786B490" >1 .14 -164 AddLeftCoclosedMonoidalEvaluationMorphismWithGivenRange</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X84635F4580F63BD0" >1 .14 -165 AddLeftCoclosedMonoidalLambdaElimination</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X83DF33EF7A19E291" >1 .14 -166 AddLeftCoclosedMonoidalLambdaIntroduction</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7954E35E784BCB8B" >1 .14 -167 AddLeftCoclosedMonoidalPostCoComposeMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7FE2EC92781C752E" >1 .14 -168 AddLeftCoclosedMonoidalPostCoComposeMorphismWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7DC17F0884BAD720" >1 .14 -169 AddLeftCoclosedMonoidalPreCoComposeMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X86DB94FE8301038C" >1 .14 -170 AddLeftCoclosedMonoidalPreCoComposeMorphismWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X829E5F7E783539C3" >1 .14 -171 AddLeftInternalCoHomOnMorphisms</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X78538C8E78635666" >1 .14 -172 AddLeftInternalCoHomOnMorphismsWithGivenLeftInternalCoHoms</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X82901BEB81D0A428" >1 .14 -173 AddLeftInternalCoHomOnObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X814CCC847F369708" >1 .14 -174 AddLeftInternalCoHomTensorProductCompatibilityMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7C3A3DEB7BA72741" >1 .14 -175 AddLeftInternalCoHomTensorProductCompatibilityMorphismWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X80C1A62B812B4565" >1 .14 -176 AddLeftInternalCoHomToTensorProductAdjunctMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X83DDE598805FFA88" >1 .14 -177 AddLeftInternalCoHomToTensorProductAdjunctMorphismWithGivenTensorProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X8104426A8327EF5E" >1 .14 -178 AddMorphismFromLeftCoBidual</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X849C36147F09B8A0" >1 .14 -179 AddMorphismFromLeftCoBidualWithGivenLeftCoBidual</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X86168FF07A697A15" >1 .14 -180 AddMorphismFromLeftInternalCoHomToTensorProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X830428C27A6BC07B" >1 .14 -181 AddMorphismFromLeftInternalCoHomToTensorProductWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7AA7EDE881098270" >1 .14 -182 AddTensorProductToLeftInternalCoHomAdjunctMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7CDB23877B3C8292" >1 .14 -183 AddTensorProductToLeftInternalCoHomAdjunctMorphismWithGivenLeftInternalCoHom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X864F1EF47CAD2BE8" >1 .14 -184 AddUniversalPropertyOfLeftCoDual</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X79CDE3B87D14EF9A" >1 .14 -185 AddAssociatorLeftToRight</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X850B5B357F592FAE" >1 .14 -186 AddAssociatorLeftToRightWithGivenTensorProducts</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X8045C4FC7B4912B4" >1 .14 -187 AddAssociatorRightToLeft</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7CF105217904D280" >1 .14 -188 AddAssociatorRightToLeftWithGivenTensorProducts</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7986052487D3CDBB" >1 .14 -189 AddLeftUnitor</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X793D2C657F19096D" >1 .14 -190 AddLeftUnitorInverse</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X87CB487587ED3EC5" >1 .14 -191 AddLeftUnitorInverseWithGivenTensorProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X8614FD9C78812C98" >1 .14 -192 AddLeftUnitorWithGivenTensorProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X8568708E7C5D8D28" >1 .14 -193 AddRightUnitor</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7B2AAD6286833F68" >1 .14 -194 AddRightUnitorInverse</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X8682171F86C6793E" >1 .14 -195 AddRightUnitorInverseWithGivenTensorProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7DB39DC9794F3FCA" >1 .14 -196 AddRightUnitorWithGivenTensorProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X83DEDFA3803035BC" >1 .14 -197 AddTensorProductOnMorphisms</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X879659397D11AD9F" >1 .14 -198 AddTensorProductOnMorphismsWithGivenTensorProducts</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7CED389B792142F5" >1 .14 -199 AddTensorProductOnObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7BC4B940858F903B" >1 .14 -200 AddTensorUnit</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X8586506084917A30" >1 .14 -201 AddCoevaluationForDual</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X831DC3947941E8BA" >1 .14 -202 AddCoevaluationForDualWithGivenTensorProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X817D08298188F2BC" >1 .14 -203 AddIsomorphismFromInternalHomToTensorProductWithDualObject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X840BC8AB7DFFD68E" >1 .14 -204 AddIsomorphismFromTensorProductWithDualObjectToInternalHom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7D2FDE687E0CB66A" >1 .14 -205 AddMorphismFromBidual</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X877C409E865C2BB3" >1 .14 -206 AddMorphismFromBidualWithGivenBidual</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X82FDEF277A71FABF" >1 .14 -207 AddMorphismFromInternalHomToTensorProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7A4A4C668706D593" >1 .14 -208 AddMorphismFromInternalHomToTensorProductWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X849B17E08679450A" >1 .14 -209 AddRankMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X798FA16B818559DB" >1 .14 -210 AddTensorProductInternalHomCompatibilityMorphismInverse</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7D9EA11980170B0C" >1 .14 -211 AddTensorProductInternalHomCompatibilityMorphismInverseWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X8446431880FFF111" >1 .14 -212 AddTraceMap</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7A3D91F87F170676" >1 .14 -213 AddCoRankMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7AA8757780D75E1F" >1 .14 -214 AddCoTraceMap</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X82087A8C7E5EBAA8" >1 .14 -215 AddCoclosedCoevaluationForCoDual</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X813CF5C07BAFD19C" >1 .14 -216 AddCoclosedCoevaluationForCoDualWithGivenTensorProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7CA7972381FC507F" >1 .14 -217 AddInternalCoHomTensorProductCompatibilityMorphismInverse</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X82F222EC80852CF1" >1 .14 -218 AddInternalCoHomTensorProductCompatibilityMorphismInverseWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X84E2048279A169A6" >1 .14 -219 AddIsomorphismFromInternalCoHomToTensorProductWithCoDualObject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7DFE79B48125A1E0" >1 .14 -220 AddIsomorphismFromTensorProductWithCoDualObjectToInternalCoHom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7F27D275849C84B2" >1 .14 -221 AddMorphismFromTensorProductToInternalCoHom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7B5706318327501E" >1 .14 -222 AddMorphismFromTensorProductToInternalCoHomWithGivenObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7EBD7033871B0F3D" >1 .14 -223 AddMorphismToCoBidual</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X867E02E07CEC5B34" >1 .14 -224 AddMorphismToCoBidualWithGivenCoBidual</a></span >div ></div >div >div class="ContChap" ><a href="chap2_mj.html#X7967FE8E7BBDF485" >2 <span class="Heading" >Examples and Tests</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2_mj.html#X7862428B781B1F3D" >2 .1 <span class="Heading" >Test functions</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X8131040685BBC24E" >2 .1 -1 AdditiveMonoidalCategoriesTest</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X803EED927C6BFB83" >2 .1 -2 TestBraidingForInvertibility</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X794ADC5E7B9ED6E9" >2 .1 -3 TestBraidingCompatibility</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X85D661D482543648" >2 .1 -4 TestBraidingCompatibilityForAllTriplesInList</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7D87D6737E0B485F" >2 .1 -5 BraidedMonoidalCategoriesTest</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7CDDEF3E87731A54" >2 .1 -6 ClosedMonoidalCategoriesTest</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7EAC790E85CC1D26" >2 .1 -7 ClosedMonoidalCategoriesTestWithGiven</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X83E919E984B367B1" >2 .1 -8 CoclosedMonoidalCategoriesTest</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7F29A16A810D390D" >2 .1 -9 CoclosedMonoidalCategoriesTestWithGiven</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7B0D72D07AAA7B9B" >2 .1 -10 LeftClosedMonoidalCategoriesTest</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7BCAE7FE7E32B70A" >2 .1 -11 LeftClosedMonoidalCategoriesTestWithGiven</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X865E82AA7FB9B0BE" >2 .1 -12 LeftCoclosedMonoidalCategoriesTest</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7BF584B6805BB8DA" >2 .1 -13 LeftCoclosedMonoidalCategoriesTestWithGiven</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7B05AB7F7BAF2B62" >2 .1 -14 MonoidalCategoriesTensorProductOnObjectsAndTensorUnitTest</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7FE8E3E581929705" >2 .1 -15 TestMonoidalUnitorsForInvertibility</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X78A123237F5F81BE" >2 .1 -16 TestAssociatorForInvertibility</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7EB6CE877FDBFAE5" >2 .1 -17 TestMonoidalTriangleIdentity</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7B0890C57F20717C" >2 .1 -18 TestMonoidalTriangleIdentityForAllPairsInList</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X8786C1FF7F09F124" >2 .1 -19 TestMonoidalPentagonIdentity</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7D45BF317D6237DC" >2 .1 -20 TestMonoidalPentagonIdentityUsingWithGivenOperations</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7E96BEF17CD1B38B" >2 .1 -21 TestMonoidalPentagonIdentityForAllQuadruplesInList</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7BCAF88A806E562D" >2 .1 -22 MonoidalCategoriesTest</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X85AB97E9788D543D" >2 .1 -23 TestZigZagIdentitiesForDual</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X78CAAAE77DC5CF4F" >2 .1 -24 RigidSymmetricClosedMonoidalCategoriesTest</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X8154BEE7850EFEEA" >2 .1 -25 RigidSymmetricCoclosedMonoidalCategoriesTest</a></span >div ></div >div >div class="ContChap" ><a href="chap3_mj.html#X7C2E370A85B0A5CB" >3 <span class="Heading" >Code Generation for Monodial Categories</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3_mj.html#X808DC49C7ED99B52" >3 .1 <span class="Heading" >Monoidal Categories</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X85C82D6A878B25DD" >3 .1 -1 WriteFileForMonoidalStructure</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3_mj.html#X7BC682067A30E580" >3 .2 <span class="Heading" >Closed Monoidal Categories</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7EF7CDED85FB1CA1" >3 .2 -1 WriteFileForClosedMonoidalStructure</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7B1E6E95839A2EB7" >3 .2 -2 WriteFileForLeftClosedMonoidalStructure</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3_mj.html#X8197D69B805349AC" >3 .3 <span class="Heading" >Coclosed Monoidal Categories</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X83DBF79278AD1D37" >3 .3 -1 WriteFileForCoclosedMonoidalStructure</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7DAEDDFF84783E19" >3 .3 -2 WriteFileForLeftCoclosedMonoidalStructure</a></span >div ></div >div >div class="ContChap" ><a href="chap4_mj.html#X84B4C3E17FDDFC55" >4 <span class="Heading" >The terminal category with multiple objects</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4_mj.html#X86EC0F0A78ECBC10" >4 .1 <span class="Heading" >Constructors</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4_mj.html#X7D03633A7D98026B" >4 .2 <span class="Heading" ><strong class="pkg" >GAP</strong > Categories</span ></a>span >div >div >div class="ContChap" ><a href="chap5_mj.html#X84EF85257973461A" >5 <span class="Heading" >Legacy Operations and Synonyms</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap5_mj.html#X7F2BBEE67CC67F03" >5 .1 <span class="Heading" >Legacy operations</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X87648A1B86BC12CD" >5 .1 -1 CoclosedCoevaluationMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X78E1EE0879D7E094" >5 .1 -2 CoclosedCoevaluationMorphismWithGivenSource</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X8013AC4C837F9828" >5 .1 -3 CoclosedEvaluationMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X84FE6ABB879495DE" >5 .1 -4 CoclosedEvaluationMorphismWithGivenRange</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X79E277047AB3E909" >5 .1 -5 CoevaluationMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7E8123AD8567A5C0" >5 .1 -6 CoevaluationMorphismWithGivenRange</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap5_mj.html#X85F14B247ED4A698" >5 .2 <span class="Heading" >Synonyms for legacy operations</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X809226D2878DD662" >5 .2 -1 EvaluationMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7E42359B7A888F61" >5 .2 -2 EvaluationMorphismWithGivenSource</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X78B6BE768607496E" >5 .2 -3 InternalCoHomToTensorProductAdjunctionMap</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7BBB6AD87A056F37" >5 .2 -4 InternalCoHomToTensorProductAdjunctionMapWithGivenTensorProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7E415A5E859935AA" >5 .2 -5 InternalHomToTensorProductAdjunctionMap</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7E89D6DA7828F99E" >5 .2 -6 InternalHomToTensorProductAdjunctionMapWithGivenTensorProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X86CB055F839F71A3" >5 .2 -7 TensorProductToInternalCoHomAdjunctionMap</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7E1C1567803E7C91" >5 .2 -8 TensorProductToInternalCoHomAdjunctionMapWithGivenInternalCoHom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X8534C5AB7B80A8D8" >5 .2 -9 TensorProductToInternalHomAdjunctionMap</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X875D98EF835CC34C" >5 .2 -10 TensorProductToInternalHomAdjunctionMapWithGivenInternalHom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7A68E9AF856E8EC5" >5 .2 -11 InternalCoHomToTensorProductLeftAdjunctionMap</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7A6128507D63055E" >5 .2 -12 InternalHomToTensorProductLeftAdjunctionMap</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7D9D52A780F6B608" >5 .2 -13 TensorProductToInternalCoHomLeftAdjunctionMap</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X814AE2D67D150C0B" >5 .2 -14 TensorProductToInternalCoHomLeftAdjunctionMapWithGivenInternalCoHom</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X782469E1837A982C" >5 .2 -15 TensorProductToInternalHomLeftAdjunctionMap</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X846E5D587AD2FB8D" >5 .2 -16 TensorProductToInternalHomLeftAdjunctionMapWithGivenInternalHom</a></span >div ></div >div >div class="ContChap" ><a href="chap6_mj.html#X806DBCCC82BE4D32" >6 <span class="Heading" >MonoidalCategories automatic generated documentation</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap6_mj.html#X86BA4B7E7B19456B" >6 .1 <span class="Heading" >MonoidalCategories automatic generated documentation of properties</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X845F43E584BE51F3" >6 .1 -1 IsAdditiveMonoidalCategory</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7EB424EE81E0290D" >6 .1 -2 IsBraidedMonoidalCategory</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X78F907177D3C4BF8" >6 .1 -3 IsClosedMonoidalCategory</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X8262914378FA0F1A" >6 .1 -4 IsCoclosedMonoidalCategory</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X861056EA7B4BFD70" >6 .1 -5 IsLeftClosedMonoidalCategory</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7D0F6DAC862788BE" >6 .1 -6 IsLeftCoclosedMonoidalCategory</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X877C15BA81C14016" >6 .1 -7 IsMonoidalCategory</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X867C0E9487F19155" >6 .1 -8 IsStrictMonoidalCategory</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7B5F85DB8497D183" >6 .1 -9 IsRigidSymmetricClosedMonoidalCategory</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7C610A4B848B53FF" >6 .1 -10 IsRigidSymmetricCoclosedMonoidalCategory</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7BE3F4D085AA0055" >6 .1 -11 IsSymmetricClosedMonoidalCategory</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X84215E5E875DD7DC" >6 .1 -12 IsSymmetricCoclosedMonoidalCategory</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X8296E9838534F4D1" >6 .1 -13 IsSymmetricMonoidalCategory</a></span >div ></div >div >div class="ContChap" ><a href="chapInd_mj.html" ><span class="Heading" >Index</span ></a></div >br />div >div class="chlinkprevnextbot" > <a href="chap0_mj.html" >[Top of Book]</a> <a href="chap0_mj.html#contents" >[Contents]</a> <a href="chap1_mj.html" >[Next Chapter]</a> </div >div class="chlinkbot" ><span class="chlink1" >Goto Chapter: </span ><a 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