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<div class="ChapSects"><a href="chap7.html#X87A9DB228112DF45">7 <span class="Heading">Add Functions</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7.html#X85EC14607B6F66FE">7.1 <span class="Heading">Functions Installed by Add</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7.html#X85E3D9E07B8BC960">7.2 <span class="Heading">Add Method</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7.html#X7E1C4F9D80329FEC">7.3 <span class="Heading">Method name record entries</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7.html#X844CF4D187364721">7.4 <span class="Heading">Enhancing the method name record</span></a>
</span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7.html#X7AFA0108870EE97C">7.5 <span class="Heading">Prepare functions</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X84409FF87D35BE99">7.5-1 CAPOperationPrepareFunction</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7843089F86F47D3B">7.5-2 CAPAddPrepareFunction</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X82AEE9507F0B48BC">7.5-3 ListCAPPrepareFunctions</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7.html#X829CEC0B8319A503">7.6 <span class="Heading">Available Add functions</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X811BB502781CFBB9">7.6-1 AddAdditionForMorphisms</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7BE108F1785F069A">7.6-2 AddAdditiveGenerators</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7AB78A707BF08401">7.6-3 AddAdditiveInverseForMorphisms</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X786682798320D413">7.6-4 AddAstrictionToCoimage</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7A3941A6808F122B">7.6-5 AddAstrictionToCoimageWithGivenCoimageObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7E995205864340BD">7.6-6 AddBasisOfExternalHom</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X8452C3617C063298">7.6-7 AddBasisOfSolutionsOfHomogeneousDoubleLinearSystemInLinearCategory</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X78FCEAFA80D1D71B">7.6-8 AddBasisOfSolutionsOfHomogeneousLinearSystemInLinearCategory</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X78C7D6E582FD41E9">7.6-9 AddCoastrictionToImage</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X8077FB7485FCD5E6">7.6-10 AddCoastrictionToImageWithGivenImageObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7F594A2F85F3806B">7.6-11 AddCoefficientsOfMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X854D668E7F7AE192">7.6-12 AddCoequalizer</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X85D135A186E19749">7.6-13 AddCoequalizerFunctorial</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X784EE97C7CBD86AE">7.6-14 AddCoequalizerFunctorialWithGivenCoequalizers</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X87747A0B87DA7CF9">7.6-15 AddCoimageObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7F38C4A17E52073B">7.6-16 AddCoimageObjectFunctorial</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X80465F7B85F144D7">7.6-17 AddCoimageObjectFunctorialWithGivenCoimageObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X85B54DD47C3E9682">7.6-18 AddCoimageProjection</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X819E76B4798EA44C">7.6-19 AddCoimageProjectionWithGivenCoimageObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7988858A83DAFF4B">7.6-20 AddCokernelColift</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7991C43079F444CC">7.6-21 AddCokernelColiftWithGivenCokernelObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7827637D7B8E7E60">7.6-22 AddCokernelObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7E982C787FDA03DC">7.6-23 AddCokernelObjectFunctorial</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7B162B6E7D60FFE7">7.6-24 AddCokernelObjectFunctorialWithGivenCokernelObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7D9723AA7E4EAC2A">7.6-25 AddCokernelProjection</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X793803DC816CBA27">7.6-26 AddCokernelProjectionWithGivenCokernelObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X84A7986F82ED769E">7.6-27 AddColift</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7BBEF7C479E612ED">7.6-28 AddColiftAlongEpimorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7F566C7D7ACC93CE">7.6-29 AddComponentOfMorphismFromCoproduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7ABE523F82B2DB7C">7.6-30 AddComponentOfMorphismFromDirectSum</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7F72750382933C68">7.6-31 AddComponentOfMorphismIntoDirectProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X82B3F4A87CDF6F87">7.6-32 AddComponentOfMorphismIntoDirectSum</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X790C5EE180471583">7.6-33 AddCoproduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X79F685258336C4B4">7.6-34 AddCoproductFunctorial</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7B23923D84D6FC9F">7.6-35 AddCoproductFunctorialWithGivenCoproducts</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7FE84F89844B8352">7.6-36 AddDirectProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X78F2B05A7DC3F890">7.6-37 AddDirectProductFunctorial</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X789E69C583A0E118">7.6-38 AddDirectProductFunctorialWithGivenDirectProducts</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7CE460A37D8D468F">7.6-39 AddDirectSum</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X80778A107EFC97B8">7.6-40 AddDirectSumFunctorial</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X829D88B6845FA373">7.6-41 AddDirectSumFunctorialWithGivenDirectSums</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7D7A07CC7C9541DB">7.6-42 AddDistinguishedObjectOfHomomorphismStructure</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X86275A2F7EF2A472">7.6-43 AddEmbeddingOfEqualizer</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X8346BE927EB0C95B">7.6-44 AddEmbeddingOfEqualizerWithGivenEqualizer</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X80D4EB9F793C19E7">7.6-45 AddEpimorphismFromProjectiveCoverObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X82D978CC78155811">7.6-46 AddEpimorphismFromProjectiveCoverObjectWithGivenProjectiveCoverObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X85B76EA67A35B7B2">7.6-47 AddEpimorphismFromSomeProjectiveObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7B7B27468506DA04">7.6-48 AddEpimorphismFromSomeProjectiveObjectWithGivenSomeProjectiveObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X8708C28287172ED7">7.6-49 AddEqualizer</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X8042AA538466FFE0">7.6-50 AddEqualizerFunctorial</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X819700097DE622A4">7.6-51 AddEqualizerFunctorialWithGivenEqualizers</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X86B7F8B983B9B184">7.6-52 AddFiberProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7BFDD60786E07890">7.6-53 AddFiberProductFunctorial</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X85CCD05C7D3D6B7C">7.6-54 AddFiberProductFunctorialWithGivenFiberProducts</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7B175A717B8D152B">7.6-55 AddHomologyObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X78E7DBF47DBDFB55">7.6-56 AddHomologyObjectFunctorialWithGivenHomologyObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X80ADD34F7833A668">7.6-57 AddHomomorphismStructureOnMorphisms</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7F6B67487C55B055">7.6-58 AddHomomorphismStructureOnMorphismsWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7833851F7DD2D0F1">7.6-59 AddHomomorphismStructureOnObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X80B2FA2F7C2E2BDA">7.6-60 AddHorizontalPostCompose</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7C759D3A7CB3FA3A">7.6-61 AddHorizontalPreCompose</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X878F4D2481E94EB6">7.6-62 AddIdentityMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X85B4A2607CDFC0D2">7.6-63 AddIdentityTwoCell</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X796EDCCD7A729E12">7.6-64 AddImageEmbedding</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X785393EB7C27451E">7.6-65 AddImageEmbeddingWithGivenImageObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7CA61123868B51B2">7.6-66 AddImageObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X8044B4EC7F102769">7.6-67 AddImageObjectFunctorial</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7B22900C82A20B49">7.6-68 AddImageObjectFunctorialWithGivenImageObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X79CC10D18746249B">7.6-69 AddIndecomposableInjectiveObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X782ED2C27FB4739D">7.6-70 AddIndecomposableProjectiveObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X78D5E19E781D696A">7.6-71 AddInitialObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X80950253819512A8">7.6-72 AddInitialObjectFunctorial</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X85493AEC80972B68">7.6-73 AddInitialObjectFunctorialWithGivenInitialObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X81B68CB6783FAFE0">7.6-74 AddInjectionOfCofactorOfCoproduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7DC2E9CD78A8622C">7.6-75 AddInjectionOfCofactorOfCoproductWithGivenCoproduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X845EB2F47C8FE49C">7.6-76 AddInjectionOfCofactorOfDirectSum</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X86A78CC2859E4382">7.6-77 AddInjectionOfCofactorOfDirectSumWithGivenDirectSum</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X87ED0E87850C6D96">7.6-78 AddInjectionOfCofactorOfPushout</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X8352461A796F9214">7.6-79 AddInjectionOfCofactorOfPushoutWithGivenPushout</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7CE0C54080533C0E">7.6-80 AddInjectiveColift</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7E7B72EC7B2FB537">7.6-81 AddInjectiveDimension</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X81CE72B78061AE51">7.6-82 AddInjectiveEnvelopeObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X805AC6057B80880D">7.6-83 AddInterpretMorphismAsMorphismFromDistinguishedObjectToHomomorphismStructure</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X79A927B187FE594C">7.6-84 AddInterpretMorphismAsMorphismFromDistinguishedObjectToHomomorphismStructureWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X87DD6A387E32DD37">7.6-85 AddInterpretMorphismFromDistinguishedObjectToHomomorphismStructureAsMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X865C7A1781F3AEF7">7.6-86 AddInverseForMorphisms</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X872C63B87BFEE476">7.6-87 AddInverseOfMorphismFromCoimageToImage</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X849DC541848114A0">7.6-88 AddInverseOfMorphismFromCoimageToImageWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7FA3BD6D79D99498">7.6-89 AddIsAutomorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X78D83890795EAAF2">7.6-90 AddIsBijectiveObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X78E046E387674019">7.6-91 AddIsCodominating</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7A41C14B8169E993">7.6-92 AddIsColiftable</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X86BF34667D329168">7.6-93 AddIsColiftableAlongEpimorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X861A83B3802D0FBD">7.6-94 AddIsCongruentForMorphisms</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X834AC612831DDD11">7.6-95 AddIsDominating</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X87B1905481F6AF28">7.6-96 AddIsEndomorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X8523850C827FE182">7.6-97 AddIsEpimorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X82DE9AE387425307">7.6-98 AddIsEqualAsFactorobjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7A97D3C3869323D1">7.6-99 AddIsEqualAsSubobjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X833165B27AA74580">7.6-100 AddIsEqualForCacheForMorphisms</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7887D32C7973F4A0">7.6-101 AddIsEqualForCacheForObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X83F60F5F7E57F3C8">7.6-102 AddIsEqualForMorphisms</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X84AB81547A770D36">7.6-103 AddIsEqualForMorphismsOnMor</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X787F654B82150781">7.6-104 AddIsEqualForObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X79F9BCED7C82AEAC">7.6-105 AddIsEqualToIdentityMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X849B7E507B01ABE7">7.6-106 AddIsEqualToZeroMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X85D7E2DE7D45CF70">7.6-107 AddIsHomSetInhabited</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X85701DBE7A5F90A1">7.6-108 AddIsIdempotent</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7E6EDA9484F3E6F6">7.6-109 AddIsInitial</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7F7F309F7C67D6CE">7.6-110 AddIsInjective</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X8783D5BB79CB2FD9">7.6-111 AddIsIsomorphicForObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7B0818ED7A7BBCB4">7.6-112 AddIsIsomorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X79AC542F8227455E">7.6-113 AddIsLiftable</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7BD695308127A877">7.6-114 AddIsLiftableAlongMonomorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X87DEC4BD7C48E679">7.6-115 AddIsMonomorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7FCC38DC7843D455">7.6-116 AddIsOne</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X865C78CF789DA86D">7.6-117 AddIsProjective</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7D7BDF8F7EED3A72">7.6-118 AddIsSplitEpimorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7C5D46B77A65ACF2">7.6-119 AddIsSplitMonomorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7EDB2D5B7F234ADA">7.6-120 AddIsTerminal</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7A4BE39A83D2A730">7.6-121 AddIsWellDefinedForMorphisms</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X861EFAFB8268CBAC">7.6-122 AddIsWellDefinedForMorphismsWithGivenSourceAndRange</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X859219147B3058B8">7.6-123 AddIsWellDefinedForObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7EE52A1587E15D94">7.6-124 AddIsWellDefinedForTwoCells</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X87DD3BD27C49450A">7.6-125 AddIsZeroForMorphisms</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X78C3E7BF78A9A7D5">7.6-126 AddIsZeroForObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7B80534F79D74B95">7.6-127 AddIsomorphismFromCoequalizerOfCoproductDiagramToPushout</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X866BBCDA84AC7C3F">7.6-128 AddIsomorphismFromCoequalizerToCokernelOfJointPairwiseDifferencesOfMorphismsFromCoproduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X80B45F4D7A7B96A4">7.6-129 AddIsomorphismFromCoimageToCokernelOfKernel</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X8236335C7EC1C0F9">7.6-130 AddIsomorphismFromCokernelOfJointPairwiseDifferencesOfMorphismsFromCoproductToCoequalizer</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7D9B059578AC42D6">7.6-131 AddIsomorphismFromCokernelOfKernelToCoimage</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X87C04FAA7F49427B">7.6-132 AddIsomorphismFromCoproductToDirectSum</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X793FDA608055E5C9">7.6-133 AddIsomorphismFromDirectProductToDirectSum</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7D710CA282194DC7">7.6-134 AddIsomorphismFromDirectSumToCoproduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X79DA06C087D4BDF3">7.6-135 AddIsomorphismFromDirectSumToDirectProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X83D3BDAF7BFBF924">7.6-136 AddIsomorphismFromEqualizerOfDirectProductDiagramToFiberProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X81719A3179D403DD">7.6-137 AddIsomorphismFromEqualizerToKernelOfJointPairwiseDifferencesOfMorphismsIntoDirectProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7FF20AFE7CE85AF5">7.6-138 AddIsomorphismFromFiberProductToEqualizerOfDirectProductDiagram</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7BD4A45087C884FD">7.6-139 AddIsomorphismFromHomologyObjectToItsConstructionAsAnImageObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7B09757B8411AD52">7.6-140 AddIsomorphismFromImageObjectToKernelOfCokernel</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X876F82038640430A">7.6-141 AddIsomorphismFromInitialObjectToZeroObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X80B2303081911753">7.6-142 AddIsomorphismFromItsConstructionAsAnImageObjectToHomologyObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X78A3EEFB843C5067">7.6-143 AddIsomorphismFromKernelOfCokernelToImageObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X80B6437D7B87933D">7.6-144 AddIsomorphismFromKernelOfJointPairwiseDifferencesOfMorphismsIntoDirectProductToEqualizer</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7C757EA67A35147A">7.6-145 AddIsomorphismFromPushoutToCoequalizerOfCoproductDiagram</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X85A29A037839B32B">7.6-146 AddIsomorphismFromTerminalObjectToZeroObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X8084DA9E870DF7DB">7.6-147 AddIsomorphismFromZeroObjectToInitialObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7BDED1CE7F0FADE9">7.6-148 AddIsomorphismFromZeroObjectToTerminalObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7A44C3757DD351AC">7.6-149 AddJointPairwiseDifferencesOfMorphismsFromCoproduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X83C624FA83037280">7.6-150 AddJointPairwiseDifferencesOfMorphismsIntoDirectProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X788D35FA8050DA84">7.6-151 AddKernelEmbedding</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X87668C2183C9E8A1">7.6-152 AddKernelEmbeddingWithGivenKernelObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7A3F184085748DE6">7.6-153 AddKernelLift</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7D6119357E10B4DA">7.6-154 AddKernelLiftWithGivenKernelObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X8681E565875A8C03">7.6-155 AddKernelObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X818A1E2C82034517">7.6-156 AddKernelObjectFunctorial</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7BE607577847C4DC">7.6-157 AddKernelObjectFunctorialWithGivenKernelObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7DA9346A8517648D">7.6-158 AddLift</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X869A19337CB3059E">7.6-159 AddLiftAlongMonomorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X851447D2876BF1D1">7.6-160 AddLinearCombinationOfMorphisms</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X80E205428725FEA7">7.6-161 AddMereExistenceOfSolutionOfLinearSystemInAbCategory</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7A635EA8808F2EC3">7.6-162 AddMereExistenceOfUniqueSolutionOfHomogeneousLinearSystemInAbCategory</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7C1910B77A78E2B8">7.6-163 AddMereExistenceOfUniqueSolutionOfLinearSystemInAbCategory</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7BD5C9B0867857CC">7.6-164 AddMonomorphismIntoInjectiveEnvelopeObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X87B801BF7F861F09">7.6-165 AddMonomorphismIntoInjectiveEnvelopeObjectWithGivenInjectiveEnvelopeObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X81C9788D7DD27D18">7.6-166 AddMonomorphismIntoSomeInjectiveObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7CCBF6577ADC62D9">7.6-167 AddMonomorphismIntoSomeInjectiveObjectWithGivenSomeInjectiveObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X873C908279759A45">7.6-168 AddMorphismBetweenDirectSums</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7E295E2784C267D5">7.6-169 AddMorphismBetweenDirectSumsWithGivenDirectSums</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7A1067568608419D">7.6-170 AddMorphismConstructor</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7ADDB80C7F9BC838">7.6-171 AddMorphismDatum</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X81F30776833F49B2">7.6-172 AddMorphismFromCoimageToImage</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7FCCF6EA7BD56684">7.6-173 AddMorphismFromCoimageToImageWithGivenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X86015A918233B365">7.6-174 AddMorphismFromEqualizerToSink</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X857FA53779546DAC">7.6-175 AddMorphismFromEqualizerToSinkWithGivenEqualizer</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X87BB71D881AFD21C">7.6-176 AddMorphismFromFiberProductToSink</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7F652D597B5298C6">7.6-177 AddMorphismFromFiberProductToSinkWithGivenFiberProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X83B7DB587851A040">7.6-178 AddMorphismFromKernelObjectToSink</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7844716879CAFB0C">7.6-179 AddMorphismFromKernelObjectToSinkWithGivenKernelObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7CC2819E868B2ACF">7.6-180 AddMorphismFromSourceToCoequalizer</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X84074D4B7E584205">7.6-181 AddMorphismFromSourceToCoequalizerWithGivenCoequalizer</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7E2024F080A442DF">7.6-182 AddMorphismFromSourceToCokernelObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X837F485E7A5E6511">7.6-183 AddMorphismFromSourceToCokernelObjectWithGivenCokernelObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7A8728957EEC0667">7.6-184 AddMorphismFromSourceToPushout</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7D880C937DDE1F34">7.6-185 AddMorphismFromSourceToPushoutWithGivenPushout</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7C37598A7F7C7413">7.6-186 AddMorphismsOfExternalHom</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7AE8C7897CB6FDF8">7.6-187 AddMultiplyWithElementOfCommutativeRingForMorphisms</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7D093D4981AC4E7F">7.6-188 AddObjectConstructor</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7EF116D57BFA80B5">7.6-189 AddObjectDatum</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X853E87F47F9FC287">7.6-190 AddPostCompose</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X85A4A74585001622">7.6-191 AddPostComposeList</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X806FBF5479DB397D">7.6-192 AddPostInverseForMorphisms</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X868C87097D322509">7.6-193 AddPreCompose</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7CE1A7FC792C6577">7.6-194 AddPreComposeList</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X85E1E8037F7353F8">7.6-195 AddPreInverseForMorphisms</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X84F5824779267907">7.6-196 AddProjectionInFactorOfDirectProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7B83D0627A2DCF93">7.6-197 AddProjectionInFactorOfDirectProductWithGivenDirectProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7B87E0308677AB17">7.6-198 AddProjectionInFactorOfDirectSum</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X81ACCDB081967CD3">7.6-199 AddProjectionInFactorOfDirectSumWithGivenDirectSum</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7BC4A40A8587EB82">7.6-200 AddProjectionInFactorOfFiberProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X822C988083A72B14">7.6-201 AddProjectionInFactorOfFiberProductWithGivenFiberProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7C76BED4827D9C28">7.6-202 AddProjectionOntoCoequalizer</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X8691E0FA7BF900F5">7.6-203 AddProjectionOntoCoequalizerWithGivenCoequalizer</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7C6B7D3A80725B9A">7.6-204 AddProjectiveCoverObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X828B50D57F3DAB71">7.6-205 AddProjectiveDimension</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7AEE24E581A44083">7.6-206 AddProjectiveLift</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X78FDEE468742E573">7.6-207 AddPushout</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X85F9FDCF7E697028">7.6-208 AddPushoutFunctorial</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X810036A887D287AC">7.6-209 AddPushoutFunctorialWithGivenPushouts</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7BC5AC807FF84905">7.6-210 AddRandomMorphismByInteger</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X84BEF31F81ABC74E">7.6-211 AddRandomMorphismByList</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7D58154C7B6478A8">7.6-212 AddRandomMorphismWithFixedRangeByInteger</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7B2266E07E2114FE">7.6-213 AddRandomMorphismWithFixedRangeByList</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X78E443767AA69703">7.6-214 AddRandomMorphismWithFixedSourceAndRangeByInteger</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7A395AEB813562EA">7.6-215 AddRandomMorphismWithFixedSourceAndRangeByList</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X80E69DF27EA33C03">7.6-216 AddRandomMorphismWithFixedSourceByInteger</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7C5DEDED7A7D5F7A">7.6-217 AddRandomMorphismWithFixedSourceByList</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X8537D28D7C878EB2">7.6-218 AddRandomObjectByInteger</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X86F6CF9382A4906A">7.6-219 AddRandomObjectByList</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X802E75BC780B365B">7.6-220 AddSetOfMorphismsOfFiniteCategory</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X836997AC786FEA72">7.6-221 AddSetOfObjectsOfCategory</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X79584C2B7AE88801">7.6-222 AddSimplifyEndo</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7E143B0B7AFED0A5">7.6-223 AddSimplifyEndo_IsoFromInputObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X8289DD3582E90412">7.6-224 AddSimplifyEndo_IsoToInputObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X82FC080B78E17869">7.6-225 AddSimplifyMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X798AA0B57BDC7891">7.6-226 AddSimplifyObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X839A072483DA4590">7.6-227 AddSimplifyObject_IsoFromInputObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7CFDA57581061E05">7.6-228 AddSimplifyObject_IsoToInputObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X78D0F3D57A70F0AA">7.6-229 AddSimplifyRange</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7FB594A37A1B8DA3">7.6-230 AddSimplifyRange_IsoFromInputObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7BC056A2866EE0FC">7.6-231 AddSimplifyRange_IsoToInputObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X800D4F4678C4B03E">7.6-232 AddSimplifySource</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7FDBB4087F652D97">7.6-233 AddSimplifySourceAndRange</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7B3E60B07AF758F7">7.6-234 AddSimplifySourceAndRange_IsoFromInputRange</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X86CEC88B82874A86">7.6-235 AddSimplifySourceAndRange_IsoFromInputSource</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7AEBD3D882FFB8A7">7.6-236 AddSimplifySourceAndRange_IsoToInputRange</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7814950A81D7A307">7.6-237 AddSimplifySourceAndRange_IsoToInputSource</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X83B7D18780C28D3F">7.6-238 AddSimplifySource_IsoFromInputObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7E67CB62821ED6AA">7.6-239 AddSimplifySource_IsoToInputObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X781C4BCA81250295">7.6-240 AddSolveLinearSystemInAbCategory</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7DFC9A568472688B">7.6-241 AddSomeInjectiveObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X825C2D98794A7378">7.6-242 AddSomeIsomorphismBetweenObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7C3AF36D86F11429">7.6-243 AddSomeProjectiveObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7EB0389487C277CE">7.6-244 AddSomeReductionBySplitEpiSummand</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7E6384988569B9CA">7.6-245 AddSomeReductionBySplitEpiSummand_MorphismFromInputRange</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X871D45CA80DAAFC2">7.6-246 AddSomeReductionBySplitEpiSummand_MorphismToInputRange</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7ECA7B0182144B81">7.6-247 AddSubtractionForMorphisms</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X853690377C4630ED">7.6-248 AddSumOfMorphisms</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7C4B4B7F8009501B">7.6-249 AddTerminalObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X82ED99F9845D2DA7">7.6-250 AddTerminalObjectFunctorial</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7A7BBCB08021B976">7.6-251 AddTerminalObjectFunctorialWithGivenTerminalObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X82B3F52779407E2F">7.6-252 AddUniversalMorphismFromCoequalizer</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7F27613984BEA3BB">7.6-253 AddUniversalMorphismFromCoequalizerWithGivenCoequalizer</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X874696508440B555">7.6-254 AddUniversalMorphismFromCoproduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7ABE731884D77899">7.6-255 AddUniversalMorphismFromCoproductWithGivenCoproduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X82AEA81280F0FE29">7.6-256 AddUniversalMorphismFromDirectSum</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X81DB161779E15937">7.6-257 AddUniversalMorphismFromDirectSumWithGivenDirectSum</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7BE632048014DB7F">7.6-258 AddUniversalMorphismFromImage</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X79813E327CAD3D99">7.6-259 AddUniversalMorphismFromImageWithGivenImageObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X808255727E365DA5">7.6-260 AddUniversalMorphismFromInitialObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7F7D9168870D7AC6">7.6-261 AddUniversalMorphismFromInitialObjectWithGivenInitialObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7ACB31A479737723">7.6-262 AddUniversalMorphismFromPushout</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X847BA99A851088A1">7.6-263 AddUniversalMorphismFromPushoutWithGivenPushout</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X873263B37942E963">7.6-264 AddUniversalMorphismFromZeroObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X8396EFB87AABCD66">7.6-265 AddUniversalMorphismFromZeroObjectWithGivenZeroObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X85DB30B982F6C564">7.6-266 AddUniversalMorphismIntoCoimage</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7D83EDB07844C0FA">7.6-267 AddUniversalMorphismIntoCoimageWithGivenCoimageObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7E4C217083150A21">7.6-268 AddUniversalMorphismIntoDirectProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X84C986C67D703457">7.6-269 AddUniversalMorphismIntoDirectProductWithGivenDirectProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7AA30E857A11AA2A">7.6-270 AddUniversalMorphismIntoDirectSum</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7E666F5683000D34">7.6-271 AddUniversalMorphismIntoDirectSumWithGivenDirectSum</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X814FACA47A759C7A">7.6-272 AddUniversalMorphismIntoEqualizer</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X872A26F678D6989B">7.6-273 AddUniversalMorphismIntoEqualizerWithGivenEqualizer</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7F7446F882DF6DA5">7.6-274 AddUniversalMorphismIntoFiberProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X84C5017486990FB2">7.6-275 AddUniversalMorphismIntoFiberProductWithGivenFiberProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X84D7DDAF835BDFA3">7.6-276 AddUniversalMorphismIntoTerminalObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X8230986A7821D9B4">7.6-277 AddUniversalMorphismIntoTerminalObjectWithGivenTerminalObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7CAC035583A3BD60">7.6-278 AddUniversalMorphismIntoZeroObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X8550CFE1804A9965">7.6-279 AddUniversalMorphismIntoZeroObjectWithGivenZeroObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7AA662D58265F658">7.6-280 AddVerticalPostCompose</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X85F4507081F229DD">7.6-281 AddVerticalPreCompose</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X824C08CE7D7FB387">7.6-282 AddZeroMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7F0111277DF3FB7E">7.6-283 AddZeroObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7C6A709286103BAE">7.6-284 AddZeroObjectFunctorial</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X826BAB7F84D9499D">7.6-285 AddZeroObjectFunctorialWithGivenZeroObjects</a></span>
</div></div>
</div>

<h3>7 <span class="Heading">Add Functions</span></h3>

<p>This section describes the overall structure of Add-functions and the functions installed by them.</p>

<p><a id="X85EC14607B6F66FE" name="X85EC14607B6F66FE"></a></p>

<h4>7.1 <span class="Heading">Functions Installed by Add</span></h4>

<p>Add functions have the following syntax:</p>


<div class="example"><pre>
DeclareOperation( "AddSomeFunc",
                  [ IsCapCategory, IsList, IsInt ] );
</pre></div>

<p>The first argument is the category to which some function (e.g. <code class="code">KernelObject</code>) is added, the second is a list containing pairs of functions and additional filters for the arguments, (e.g. if one argument is a morphism, an additional filter could be <code class="code">IsMomomorphism</code>). The third is an optional weight which will then be the weight for <code class="code">SomeFunc</code> (default value: 100). This is described later. If only one function is to be installed, the list can be replaced by the function. CAP installs the given function(s) as methods for <code class="code">SomeFunc</code> (resp. <code class="code">SomeFuncOp</code> if <code class="code">SomeFunc</code> is not an operation).</p>

<p>All installed methods follow the following steps, described below:</p>


<ul>
<li><p>Redirect function</p>

</li>
<li><p>Prefunction</p>

</li>
<li><p>Function</p>

</li>
<li><p>Logic</p>

</li>
<li><p>Postfunction</p>

</li>
<li><p>Addfunction</p>

</li>
</ul>
<p>Every other part, except from function, does only depend on the name <code class="code">SomeFunc</code>. We now explain the steps in detail.</p>


<ul>
<li><p>Redirect function: The redirect is used to redirect the computation from the given functions to some other symbol. If there is for example a with given method for some universal property, and the universal object is already computed, the redirect function might detect such a thing, calls the with given operation with the universal object as additional argument and then returns the value. In general, the redirect can be an arbitrary function. It is called with the same arguments as the operation <code class="code">SomeFunc</code> itself and can return an array containing <code class="code">[ true, something ]</code>, which will cause the installed method to simply return the object <code class="code">something</code>, or <code class="code">[ false ]</code>. If the output is <code class="code">false</code>, the computation will continue with the step Prefunction.</p>

</li>
</ul>

<ul>
<li><p>Prefunction: The prefunction should be used for error handling and plausibility checks of the input to <code class="code">SomeFunc</code> (e.g. for <code class="code">KernelLift</code> it should check wether range and source of the morphims coincide). Generally, the prefunction is defined in the method record and only depends on the name <code class="code">SomeFunc</code>. It is called with the same input as the function itself, and should return either <code class="code">[ true ]</code>, which continues the computation, or <code class="code">[ false, "message" ]</code>, which will cause an error with message <code class="code">"message"</code> and some additional information.</p>

</li>
</ul>

<ul>
<li><p>Full prefunction: The full prefuction has the same semantics as the prefunction, but can perform additional, very costly checks. They are disabled by default.</p>

</li>
</ul>

<ul>
<li><p>Function: This will launch the function(s) given as arguments. The result should be as specified in the type of <code class="code">SomeFunc</code>. The resulting object is now named the result.</p>

</li>
</ul>

<ul>
<li><p>Logic: For every function, some logical todos can be implemented in a logic texfile for the category. If there is some logic written down in a file belonging to the category, or belonging to some type of category. Please see the description of logic for more details. If there is some logic and some predicate relations for the function <code class="code">SomeFunc</code>, it is installed in this step for the result.</p>

</li>
</ul>

<ul>
<li><p>Postfunction: The postfunction called with the arguments of the function and the result. It can be an arbitrary function doing some cosmetics. If for example <code class="code">SomeFunc</code> is <code class="code">KernelEmbedding</code>, it will set the <code class="code">KernelObject</code> of the input morphism to result. The postfunction is also taken from the method record and does only depend on the name <code class="code">SomeFunc</code>.</p>

</li>
</ul>

<ul>
<li><p>Addfunction: If the result is a category cell, it is added to the category for which the function was installed. This is disabled by default and can be enabled via <code class="func">EnableAddForCategoricalOperations</code> (<a href="chap1.html#X7C01E3727D08D219"><span class="RefLink">1.12-1</span></a>).</p>

</li>
</ul>
<p><a id="X85E3D9E07B8BC960" name="X85E3D9E07B8BC960"></a></p>

<h4>7.2 <span class="Heading">Add Method</span></h4>

<p>Except from installing a new method for the name <code class="code">SomeFunc</code>, an Add method does slightly more. Every Add method has the same structure. The steps in the Add method are as follows:</p>


<ul>
<li><p>Default weight: If the weight parameter is -1, the default weight is assumed, which is 100.</p>

</li>
</ul>

<ul>
<li><p>Weight check: If the current weight of the operation is lower than the given weight of the new functions, then the add function returns and installs nothing.</p>

</li>
</ul>

<ul>
<li><p>Installation: Next, the method to install the functions is created. It creates the correct filter list, by merging the standard filters for the operation with the particular filters for the given functions, then installs the method as described above.</p>

</li>
</ul>
<p>After calling an add method, the corresponding operation is available in the category. Also, some derivations, which are triggered by the setting of the primitive value, might be available.</p>

<p><a id="X7E1C4F9D80329FEC" name="X7E1C4F9D80329FEC"></a></p>

<h4>7.3 <span class="Heading">Method name record entries</span></h4>

<p>The entries of method name records can have the following components:</p>


<div class="example"><pre>
    [
        "filter_list",
        "input_arguments_names",
        "return_type",
        "output_source_getter_string",
        "output_source_getter_preconditions",
        "output_range_getter_string",
        "output_range_getter_preconditions",
        "with_given_object_position",
        "dual_operation",
        "dual_arguments_reversed",
        "dual_with_given_objects_reversed",
        "dual_preprocessor_func",
        "dual_preprocessor_func_string",
        "dual_postprocessor_func",
        "dual_postprocessor_func_string",
        "functorial",
        "compatible_with_congruence_of_morphisms",
        "redirect_function",
        "pre_function",
        "pre_function_full",
        "post_function",
    ]
</pre></div>


<ul>
<li><p>pre_function (optional): A function which is used as the prefunction of the installed methods, as described above. Can also be the name of another operation. In this case the pre function of the referenced operation is used.</p>

</li>
</ul>

<ul>
<li><p>pre_function_full (optional): A function which is used as the full prefunction of the installed methods, as described above. Can also be the name of another operation. In this case the full pre function of the referenced operation is used.</p>

</li>
</ul>

<ul>
<li><p>redirect_function (optional): A function which is used as the redirect function of the installed methods, as described above. Can also be the name of another operation. In this case the redirect function of the referenced operation is used.</p>

</li>
</ul>

<ul>
<li><p>post_function (optional): A function which is used as the postfunction of the installed methods, as described above.</p>

</li>
</ul>

<ul>
<li><p>filter_list: A list containing the basic filters for the methods installed by the add methods. Possible entries are filters, or the strings listed below, which will be replaced by appropriate filters at the time the add method is called. The first entry of <code class="code">filter_list</code> must be the string <code class="code">category</code>. If the category can be inferred from the remaining arguments, a convenience method without the category as the first argument is installed automatically.</p>


<ul>
<li><p><code class="code">category</code>,</p>

</li>
<li><p><code class="code">object</code>,</p>

</li>
<li><p><code class="code">morphism</code>,</p>

</li>
<li><p><code class="code">twocell</code>,</p>

</li>
<li><p><code class="code">object_in_range_category_of_homomorphism_structure</code>,</p>

</li>
<li><p><code class="code">morphism_in_range_category_of_homomorphism_structure</code>,</p>

</li>
<li><p><code class="code">list_of_objects</code>,</p>

</li>
<li><p><code class="code">list_of_morphisms</code>,</p>

</li>
<li><p><code class="code">list_of_twocells</code>.</p>

</li>
</ul>
</li>
</ul>

<ul>
<li><p>return_type: The return type can either be a filter or one of the strings in the list below. For objects, morphisms and <span class="Math">2</span>-cells the correct <code class="code">Add</code> function (see above) is used for the result of the computation. Otherwise, no <code class="code">Add</code> function is used after all.</p>

</li>
</ul>

<div class="example"><pre>
    [
        "object",
        "morphism",
        "twocell",
        "object_in_range_category_of_homomorphism_structure",
        "morphism_in_range_category_of_homomorphism_structure",
        "bool",
        "list_of_objects",
        "list_of_morphisms",
        "list_of_lists_of_morphisms",
        "object_datum",
        "morphism_datum",
        "nonneg_integer_or_infinity",
        "list_of_elements_of_commutative_ring_of_linear_structure",
    ]
</pre></div>


<ul>
<li><p>functorial (optional): If an object has a corresponding functorial function, e.g., <code class="code">KernelObject</code> and <code class="code">KernelObjectFunctorial</code>, the name of the functorial is stored as a string.</p>

</li>
</ul>

<ul>
<li><p>dual_operation (optional): Name of the dual operation.</p>

</li>
</ul>

<ul>
<li><p>dual_arguments_reversed (optional): Boolean, marks whether for the call of the dual operation all arguments have to be given in reversed order.</p>

</li>
</ul>

<ul>
<li><p>dual_with_given_objects_reversed (optional): Boolean, marks whether for the call of the dual operation the source and range of a with given operation have to be given in reversed order.</p>

</li>
</ul>

<ul>
<li><p>dual_preprocessor_func[_string] (optional): let f be an operation with dual operation g. For the automatic installation of g from f, the arguments given to g are preprocessed by this given function. The function can also be given as a string.</p>

</li>
</ul>

<ul>
<li><p>dual_postprocessor_func[_string] (optional): let f be an operation with dual operation g. For the automatic installation of g from f, the computed value of f is postprocessed by the given function. The function can also be given as a string.</p>

</li>
</ul>

<ul>
<li><p>input_arguments_names (optional): A duplicate free list (of the same length as <code class="code">filter_list</code>) of strings. For example, these strings will be used as the names of the arguments when automatically generating functions for this operation, e.g. in the opposite category.</p>

</li>
</ul>

<ul>
<li><p>output_source_getter_string (optional): Only valid if the operation returns a morphism: a piece of GAP code which computes the source of the returned morphism. The input arguments are available via the names given in <code class="code">input_arguments_names</code>.</p>

</li>
</ul>

<ul>
<li><p>output_source_getter_preconditions (optional): Only valid if output_source_getter_string is set: The preconditions of output_source_getter_string in the same form as preconditions of derivations but with the CAP operations given as strings.</p>

</li>
</ul>

<ul>
<li><p>output_range_getter_string (optional): Only valid if the operation returns a morphism: a piece of GAP code which computes the range of the returned morphism. The input arguments are available via the names given in <code class="code">input_arguments_names</code>.</p>

</li>
</ul>

<ul>
<li><p>output_range_getter_preconditions (optional): Only valid if output_range_getter_string is set: The preconditions of output_range_getter_string in the same form as preconditions of derivations but with the CAP operations given as strings.</p>

</li>
</ul>

<ul>
<li><p>with_given_object_position (optional): One of the following strings: <code class="code">"Source"</code>, <code class="code">"Range"</code>, or <code class="code">"both"</code>. Set for the without given operation in a with given pair. Describes whether the source resp. range are given (as the last argument of the with given operation) or both (as the second and the last argument of the with given operation).</p>

</li>
</ul>

<ul>
<li><p>compatible_with_congruence_of_morphisms (optional): Indicates if the operation is compatible with the congruence of morphisms, that is, if the output does not change with regard to <code class="code">IsEqualForObjects</code> and <code class="code">IsCongruentForMorphisms</code> if the input changes with regard to <code class="code">IsEqualForObjects</code> and <code class="code">IsCongruentForMorphisms</code>.</p>

</li>
</ul>
<p><a id="X844CF4D187364721" name="X844CF4D187364721"></a></p>

<h4>7.4 <span class="Heading">Enhancing the method name record</span></h4>

<p>The function CAP_INTERNAL_ENHANCE_NAME_RECORD can be applied to a method name record to make the following enhancements:</p>


<ul>
<li><p>Function name: Set the component function_name to the entry name.</p>

</li>
</ul>

<ul>
<li><p>WithGiven special case: If the current entry belongs to a WithGiven operation or its without given pair, the with_given_without_given_name_pair is set. Additionally, the with given flag of the WithGiven operation is set to true.</p>

</li>
</ul>

<ul>
<li><p>Redirect and post functions are created for all operations belonging to universal constructions (e.g. <code class="code">KernelLift</code>) which are not a WithGiven operation.</p>

</li>
</ul>
<p><a id="X7AFA0108870EE97C" name="X7AFA0108870EE97C"></a></p>

<h4>7.5 <span class="Heading">Prepare functions</span></h4>

<p><a id="X84409FF87D35BE99" name="X84409FF87D35BE99"></a></p>

<h5>7.5-1 CAPOperationPrepareFunction</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ CAPOperationPrepareFunction</code>( <var class="Arg">prepare_function</var>, <var class="Arg">category</var>, <var class="Arg">func</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Returns: a function</p>

<p>Given a non-CAP-conform function for any of the categorical operations, i.e., a function that computes the direct sum of two objects instead of a list of objects, this function wraps the function with a wrapper function to fit in the CAP context. For the mentioned binary direct sum one can call this function with <code class="code">"BinaryDirectSumToDirectSum"</code> as <var class="Arg">prepare_function</var>, the category, and the binary direct sum function. The function then returns a function that can be used for the direct sum categorical operation.</p>

<p>Note that <var class="Arg">func</var> is not handled by the CAP caching mechanism and that the use of prepare functions is incompatible with <code class="code">WithGiven</code> operations. Thus, one has to ensure manually that the equality and typing specifications are fulfilled.</p>

<p><a id="X7843089F86F47D3B" name="X7843089F86F47D3B"></a></p>

<h5>7.5-2 CAPAddPrepareFunction</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ CAPAddPrepareFunction</code>( <var class="Arg">prepare_function</var>, <var class="Arg">name</var>, <var class="Arg">doc_string</var>[, <var class="Arg">precondition_list</var>] )</td><td class="tdright">( function )</td></tr></table></div>
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