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<h1>GeneralizedMorphismsForCAP</h1>


<h2>Implementations of generalized morphisms for the CAP project</h2>

<p>
    2025.08-01</p>

<p>
    25 August 2025
  </p>

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<p><b>
    Sebastian Gutsche




  </b>
<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="https://sebasguts.github.io/">https://sebasguts.github.io/</a></span>
<br />Address: <br />Department Mathematik<br /> Universität Siegen<br /> Walter-Flex-Straße 3<br /> 57068 Siegen<br /> Germany<br />
</p><p><b>
    Sebastian Posur




  </b>
<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="https://sebastianpos.github.io">https://sebastianpos.github.io</a></span>
<br />Address: <br />Department Mathematik<br /> Universität Siegen<br /> Walter-Flex-Straße 3<br /> 57068 Siegen<br /> Germany<br />
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<p><a id="X8537FEB07AF2BEC8" name="X8537FEB07AF2BEC8"></a></p>

<div class="contents">
<h3>Contents<a id="contents" name="contents"></a></h3>

<div class="ContChap"><a href="chap1_mj.html#X7BD6D8987DF55657">1 <span class="Heading">Generalized Morphism Category</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1_mj.html#X7D03633A7D98026B">1.1 <span class="Heading">GAP Categories</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X79F2D53F7B79450C">1.1-1 IsGeneralizedMorphismCategory</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X7BEE0C4D8324D332">1.1-2 IsGeneralizedMorphismCategoryObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X805BE326803873AC">1.1-3 IsGeneralizedMorphism</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1_mj.html#X7C701DBF7BAE649A">1.2 <span class="Heading">Attributes</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X78C35DEB7A844B1D">1.2-1 UnderlyingHonestObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X7E72DC48842AFA58">1.2-2 DomainEmbedding</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X86B43E60846202CA">1.2-3 GeneralizedImageEmbedding</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X7EF102897D38A0CE">1.2-4 DefectEmbedding</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X834716A87EADE83E">1.2-5 GeneralizedKernelEmbedding</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X867950C684A50A6E">1.2-6 CodomainProjection</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X80E5FD8C84054135">1.2-7 GeneralizedCokernelProjection</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X7E323705780A7472">1.2-8 CodefectProjection</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X7E0DAE747945216A">1.2-9 GeneralizedCoimageProjection</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X8056D2E886060EB7">1.2-10 AssociatedMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X7CF4DA3478101045">1.2-11 DomainAssociatedMorphismCodomainTriple</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X8129D15C87A5642B">1.2-12 HonestRepresentative</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X8180D14B85D8DDFD">1.2-13 GeneralizedInverse</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X87BA1A897A3019B0">1.2-14 IdempotentDefinedBySubobject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X7F3F851D7FD6BE60">1.2-15 IdempotentDefinedByFactorobject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X8387D5C484A26089">1.2-16 UnderlyingHonestCategory</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1_mj.html#X7DE8E16C7C2D387B">1.3 <span class="Heading">Operations</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X82FE8F3E84432929">1.3-1 GeneralizedMorphismFromFactorToSubobject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X7B8E3FBC82429136">1.3-2 CommonRestriction</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X83CB98F3783972DE">1.3-3 ConcatenationProduct</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1_mj.html#X871597447BB998A1">1.4 <span class="Heading">Properties</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X78B6216F7869E215">1.4-1 IsHonest</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X806C879182E335B6">1.4-2 HasFullDomain</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X7A5A03577DF86A1F">1.4-3 HasFullCodomain</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X7B025572785DACBA">1.4-4 IsSingleValued</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X85E05A137F6C759A">1.4-5 IsTotal</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1_mj.html#X7B40ED8B78D067A5">1.5 <span class="Heading">Convenience methods</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X8276ADE97D53B8F0">1.5-1 GeneralizedMorphismCategory</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X846BEA5784436575">1.5-2 GeneralizedMorphismObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X7F89465C80D5CB2F">1.5-3 AsGeneralizedMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X7BCAEAEC78CE8093">1.5-4 GeneralizedMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X87C5A2AC86D384BC">1.5-5 GeneralizedMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X7DC1AF448411DFCE">1.5-6 GeneralizedMorphismWithRangeAid</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X7D32834C7EA50379">1.5-7 GeneralizedMorphismWithSourceAid</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap2_mj.html#X87EB52217E1FF49C">2 <span class="Heading">Generalized Morphism Category by Cospans</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X7D03633A7D98026B">2.1 <span class="Heading">GAP Categories</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X8187BB8479575083">2.1-1 IsGeneralizedMorphismCategoryByCospans</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X86C1877D7EC9F075">2.1-2 IsGeneralizedMorphismCategoryByCospansObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X82D8F9C38330F81E">2.1-3 IsGeneralizedMorphismByCospan</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X871597447BB998A1">2.2 <span class="Heading">Properties</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X815D6FE986CC3F99">2.2-1 HasIdentityAsReversedArrow</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X7C701DBF7BAE649A">2.3 <span class="Heading">Attributes</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7D7E0AB87D8C6BE4">2.3-1 UnderlyingHonestObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7863825F85197D30">2.3-2 Arrow</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X871D3BBC7E6B544B">2.3-3 ReversedArrow</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7DCA5A8278F4C569">2.3-4 NormalizedCospanTuple</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7F4AC0FE847140A4">2.3-5 PseudoInverse</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X87E4921884F9F1FF">2.3-6 GeneralizedInverseByCospan</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7CFE9A12793AF805">2.3-7 IdempotentDefinedBySubobjectByCospan</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X8330AB9480BC933A">2.3-8 IdempotentDefinedByFactorobjectByCospan</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7B636E0D7A9FA235">2.3-9 NormalizedCospan</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X7DE8E16C7C2D387B">2.4 <span class="Heading">Operations</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7988FD538374DC5C">2.4-1 GeneralizedMorphismFromFactorToSubobjectByCospan</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X86EC0F0A78ECBC10">2.5 <span class="Heading">Constructors</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X8313697F833CA064">2.5-1 GeneralizedMorphismByCospan</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X865028F47CB5A9FA">2.5-2 GeneralizedMorphismByCospan</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7B744FE28475F25B">2.5-3 GeneralizedMorphismByCospanWithSourceAid</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X79F31F9E80A5BFAD">2.5-4 AsGeneralizedMorphismByCospan</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X879C3A4F82EC9C13">2.5-5 GeneralizedMorphismCategoryByCospans</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X81ADB9C17D822C05">2.5-6 GeneralizedMorphismByCospansObject</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X83F3C1E6877018D8">2.6 <span class="Heading">Constructors of lifts of exact functors and natrual (iso)morphisms</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7A094900868E02F1">2.6-1 AsGeneralizedMorphismByCospan</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap3_mj.html#X7D54782279124748">3 <span class="Heading">Generalized Morphism Category by Spans</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X7D03633A7D98026B">3.1 <span class="Heading">GAP Categories</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7B3EA2C279A4F9E4">3.1-1 IsGeneralizedMorphismCategoryBySpans</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X78F2B8E882ECF61E">3.1-2 IsGeneralizedMorphismCategoryBySpansObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7A5BDCEE78549DFB">3.1-3 IsGeneralizedMorphismBySpan</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X871597447BB998A1">3.2 <span class="Heading">Properties</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7A058F5C7F7116DB">3.2-1 HasIdentityAsReversedArrow</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X7C701DBF7BAE649A">3.3 <span class="Heading">Attributes</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7BDCF7FD7EAE01C3">3.3-1 UnderlyingHonestObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X83C847FC86AB508B">3.3-2 Arrow</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X826CC0B57D6F7F3B">3.3-3 ReversedArrow</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X8082EEE27FB449E5">3.3-4 NormalizedSpanTuple</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X878EE24487756BD4">3.3-5 PseudoInverse</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X800786037C19DEF5">3.3-6 GeneralizedInverseBySpan</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7B8C00217DD3A64C">3.3-7 IdempotentDefinedBySubobjectBySpan</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X82D0B42E8413A5FE">3.3-8 IdempotentDefinedByFactorobjectBySpan</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X86499E0D83A9D090">3.3-9 NormalizedSpan</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X7DE8E16C7C2D387B">3.4 <span class="Heading">Operations</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7D3675B0866191EC">3.4-1 GeneralizedMorphismFromFactorToSubobjectBySpan</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X86EC0F0A78ECBC10">3.5 <span class="Heading">Constructors</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X83FA5A4C787261DB">3.5-1 GeneralizedMorphismBySpan</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7EAF87447D2A08EE">3.5-2 GeneralizedMorphismBySpan</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X79A8B50C7EB5ADE2">3.5-3 GeneralizedMorphismBySpanWithRangeAid</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X79C48BB782BD799F">3.5-4 AsGeneralizedMorphismBySpan</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X812CBF7580098CCF">3.5-5 GeneralizedMorphismCategoryBySpans</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X817694F38145FD9F">3.5-6 GeneralizedMorphismBySpansObject</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap4_mj.html#X7F39133179F83B50">4 <span class="Heading">Generalized Morphism Category by Three Arrows</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X7D03633A7D98026B">4.1 <span class="Heading">GAP Categories</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X869A7C2A85C2743A">4.1-1 IsGeneralizedMorphismCategoryByThreeArrows</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7E861596801CA565">4.1-2 IsGeneralizedMorphismCategoryByThreeArrowsObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X87934BAA84C6E654">4.1-3 IsGeneralizedMorphismByThreeArrows</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X871597447BB998A1">4.2 <span class="Heading">Properties</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X8247F41681D15233">4.2-1 HasIdentitiesAsReversedArrows</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X8347A40179DBD909">4.2-2 HasIdentityAsSourceAid</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X81F0F4FA78F9F361">4.2-3 HasIdentityAsRangeAid</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X7C701DBF7BAE649A">4.3 <span class="Heading">Attributes</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X8028877F819A0DBF">4.3-1 UnderlyingHonestObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7B17B7587A449B8E">4.3-2 SourceAid</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X87B0A0AF84F8AF7D">4.3-3 RangeAid</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7CCBCD5385E55586">4.3-4 Arrow</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X784C006B8525E205">4.3-5 PseudoInverse</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X78A8A55883C06AB1">4.3-6 GeneralizedInverseByThreeArrows</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X80E329707BAA3B29">4.3-7 IdempotentDefinedBySubobjectByThreeArrows</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X8217014B870B3EC2">4.3-8 IdempotentDefinedByFactorobjectByThreeArrows</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X7DE8E16C7C2D387B">4.4 <span class="Heading">Operations</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X78C1A22D86943E97">4.4-1 GeneralizedMorphismFromFactorToSubobjectByThreeArrows</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7A50AC43855B33B1">4.4-2 CommonCoastriction</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X86EC0F0A78ECBC10">4.5 <span class="Heading">Constructors</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X8477D6E679E15474">4.5-1 GeneralizedMorphismByThreeArrows</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7D60D9F97A2F7D5F">4.5-2 GeneralizedMorphismByThreeArrowsWithSourceAid</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7F9E6B188755170A">4.5-3 GeneralizedMorphismByThreeArrowsWithRangeAid</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7E0CF2A87AC08A8B">4.5-4 AsGeneralizedMorphismByThreeArrows</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X8296606484DDDF6C">4.5-5 GeneralizedMorphismCategoryByThreeArrows</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X8165802A8625467E">4.5-6 GeneralizedMorphismByThreeArrowsObject</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap5_mj.html#X83C47FBC7D238AD6">5 <span class="Heading">Conversion functors for generalized morphisms</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X7FBE737787FB4785">5.1 <span class="Heading">Functors from Cospans</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X79C6FF647D725997">5.1-1 FunctorFromCospansToThreeArrows</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X8092A53484B9D89E">5.1-2 FunctorFromCospansToSpans</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X828C320C7CE9AAEF">5.2 <span class="Heading">Functors from Spans</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7A250CED7862BD61">5.2-1 FunctorFromSpansToThreeArrows</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X80EAF5547D5E3A08">5.2-2 FunctorFromSpansToCospans</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X79688A9387244A81">5.3 <span class="Heading">Functors from Three Arrows</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X805E300E7CBA3F18">5.3-1 FunctorFromThreeArrowsToCospans</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7E0E745085802E80">5.3-2 FunctorFromThreeArrowsToSpans</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap6_mj.html#X877B8C39873C2938">6 <span class="Heading">Serre Quotients Subcategory</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6_mj.html#X78289A737AF28B39">6.1 <span class="Heading">implementation</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7C2C5BC07CABE97D">6.1-1 FullSubcategoryByMembershipFunction</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap7_mj.html#X7E44E8FA8790C32A">7 <span class="Heading">Serre Quotients</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7_mj.html#X7AB3D4ED7A4EF781">7.1 <span class="Heading">General operations</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7BC5B052783425A2">7.1-1 IsSerreQuotientCategoryObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X82C2C3C27C0FC106">7.1-2 IsSerreQuotientCategoryMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X8311C69E7FEEF417">7.1-3 SerreQuotientCategory</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7B2E75C3828CFEE4">7.1-4 AsSerreQuotientCategoryObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X8228022A7EB4CB66">7.1-5 SerreQuotientCategoryMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7C93747782930A14">7.1-6 SerreQuotientCategoryMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7FF1277C81BAD87E">7.1-7 SerreQuotientCategoryMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7BD12BC6873CB655">7.1-8 SerreQuotientCategoryMorphismWithSourceAid</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X8461E2707FCF6EB0">7.1-9 SerreQuotientCategoryMorphismWithRangeAid</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7C2D68DA796082CE">7.1-10 AsSerreQuotientCategoryMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7F51A2A678518D91">7.1-11 SubcategoryMembershipTestFunctionForSerreQuotient</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X8387D5C484A26089">7.1-12 UnderlyingHonestCategory</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7B0FD44F7FA4F8C1">7.1-13 UnderlyingGeneralizedMorphismCategory</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X86E915208420C01C">7.1-14 UnderlyingGeneralizedObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X812EDC687898EEBF">7.1-15 UnderlyingHonestObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7E403ABA78261622">7.1-16 UnderlyingGeneralizedMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7A1765BF783041DC">7.1-17 CanonicalProjection</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7_mj.html#X87F6FB587AA54985">7.2 <span class="Heading">Serre quotients by cospans</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7B0DFAB77891EB63">7.2-1 SerreQuotientCategoryByCospans</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7C696E9E83CA9250">7.2-2 AsSerreQuotientCategoryByCospansObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7F1CBD4F82097FFE">7.2-3 SerreQuotientCategoryByCospansMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7B6DB3178122E617">7.2-4 SerreQuotientCategoryByCospansMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X84649E8381E40A5E">7.2-5 SerreQuotientCategoryByCospansMorphismWithSourceAid</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X8163B686820C8119">7.2-6 SerreQuotientCategoryByCospansMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X83B53BAD85CDABE3">7.2-7 AsSerreQuotientCategoryByCospansMorphism</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7_mj.html#X7E8AEC567A971ABF">7.3 <span class="Heading">Serre Quotients by Spans</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X81B80C5882061F37">7.3-1 SerreQuotientCategoryBySpans</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X82726E3C7A66996A">7.3-2 AsSerreQuotientCategoryBySpansObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X8540DCE084BB710F">7.3-3 SerreQuotientCategoryBySpansMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X854E2C577EBC71A8">7.3-4 SerreQuotientCategoryBySpansMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X85320AF0799B2ED6">7.3-5 SerreQuotientCategoryBySpansMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7BF244A67D0A7199">7.3-6 SerreQuotientCategoryBySpansMorphismWithRangeAid</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X838E9D4D7BF0AA85">7.3-7 AsSerreQuotientCategoryBySpansMorphism</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7_mj.html#X8718215E7B950D7C">7.4 <span class="Heading">Serre Quotients modeled by three arrows</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X856C35F28411363D">7.4-1 SerreQuotientCategoryByThreeArrows</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X80BDE2C9864D84B8">7.4-2 AsSerreQuotientCategoryByThreeArrowsObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7E798D6882E5DBB4">7.4-3 SerreQuotientCategoryByThreeArrowsMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7AAB402C852E6030">7.4-4 SerreQuotientCategoryByThreeArrowsMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X8597A92278BC8D63">7.4-5 SerreQuotientCategoryByThreeArrowsMorphismWithSourceAid</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X820FF6B88188DB68">7.4-6 SerreQuotientCategoryByThreeArrowsMorphismWithRangeAid</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7DFC91D07E9A187B">7.4-7 AsSerreQuotientCategoryByThreeArrowsMorphism</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap8_mj.html#X79D7DBA7827EFB86">8 <span class="Heading">Serre Quotients Functors</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap8_mj.html#X78D1062D78BE08C1">8.1 <span class="Heading">Functors</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8_mj.html#X873A67F482BA7BFD">8.1-1 SerreQuotientConversionFunctor</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap9_mj.html#X7967FE8E7BBDF485">9 <span class="Heading">Examples and Tests</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9_mj.html#X8104A77D7B5CCD4F">9.1 <span class="Heading">Basic Commands</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9_mj.html#X8769971A878B6648">9.2 <span class="Heading">Intersection of Nodal Curve and Cusp</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9_mj.html#X8245BF297DF9A3E7">9.3 <span class="Heading">WrapperCategory</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9_mj.html#X8325B23C86E16E76">9.4 <span class="Heading">Sweep</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9_mj.html#X86FB477C7908A3A6">9.5 <span class="Heading">Generalized Morphisms Category</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9_mj.html#X7E8AFE5085FF7E15">9.6 <span class="Heading">IsWellDefined</span></a>
</span>
</div>
</div>
<div class="ContChap"><a href="chapInd_mj.html"><span class="Heading">Index</span></a></div>
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