<?xml version="1.0" encoding="UTF-8" ?>DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd " >html xmlns="http://www.w3.org/1999/xhtml " xml:lang="en" >head >title >GAP (GeneralizedMorphismsForCAP) - Contents</title >meta http-equiv="content-type" content="text/html; charset=UTF-8" />meta name="generator" content="GAPDoc2HTML" />link rel="stylesheet" type="text/css" href="manual.css" />script src="manual.js" type="text/javascript" ></script >script type="text/javascript" >overwriteStyle();</script >head >body class="chap0" onload="jscontent()" >div class="chlinktop" ><span class="chlink1" >Goto Chapter: </span ><a href="chap0.html" >Top</a> <a href="chap1.html" >1</a> <a href="chap2.html" >2</a> <a href="chap3.html" >3</a> <a href="chap4.html" >4</a> <a href="chap5.html" >5</a> <a href="chap6.html" >6</a> <a href="chap7.html" >7</a> <a href="chap8.html" >8</a> <a href="chap9.html" >9</a> <a href="chapInd.html" >Ind</a> </div >div class="chlinkprevnexttop" > <a href="chap0.html" >[Top of Book]</a> <a href="chap0.html#contents" >[Contents]</a> <a href="chap1.html" >[Next Chapter]</a> </div >"mathjaxlink" class="pcenter" ><a href="chap0_mj.html" >[MathJax on]</a></p>"X7D2C85EC87DD46E5" name="X7D2C85EC87DD46E5" ></a></p>div class="pcenter" >h1 >GeneralizedMorphismsForCAP</h1 >div >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 />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 />"X8537FEB07AF2BEC8" name="X8537FEB07AF2BEC8" ></a></p>div class="contents" >"contents" name="contents" ></a></h3>div class="ContChap" ><a href="chap1.html#X7BD6D8987DF55657" >1 <span class="Heading" >Generalized Morphism Category</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap1.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.html#X79F2D53F7B79450C" >1.1-1 IsGeneralizedMorphismCategory</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X7BEE0C4D8324D332" >1.1-2 IsGeneralizedMorphismCategoryObject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X805BE326803873AC" >1.1-3 IsGeneralizedMorphism</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap1.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.html#X78C35DEB7A844B1D" >1.2-1 UnderlyingHonestObject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X7E72DC48842AFA58" >1.2-2 DomainEmbedding</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X86B43E60846202CA" >1.2-3 GeneralizedImageEmbedding</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X7EF102897D38A0CE" >1.2-4 DefectEmbedding</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X834716A87EADE83E" >1.2-5 GeneralizedKernelEmbedding</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X867950C684A50A6E" >1.2-6 CodomainProjection</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X80E5FD8C84054135" >1.2-7 GeneralizedCokernelProjection</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X7E323705780A7472" >1.2-8 CodefectProjection</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X7E0DAE747945216A" >1.2-9 GeneralizedCoimageProjection</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X8056D2E886060EB7" >1.2-10 AssociatedMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X7CF4DA3478101045" >1.2-11 DomainAssociatedMorphismCodomainTriple</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X8129D15C87A5642B" >1.2-12 HonestRepresentative</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X8180D14B85D8DDFD" >1.2-13 GeneralizedInverse</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X87BA1A897A3019B0" >1.2-14 IdempotentDefinedBySubobject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X7F3F851D7FD6BE60" >1.2-15 IdempotentDefinedByFactorobject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X8387D5C484A26089" >1.2-16 UnderlyingHonestCategory</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap1.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.html#X82FE8F3E84432929" >1.3-1 GeneralizedMorphismFromFactorToSubobject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X7B8E3FBC82429136" >1.3-2 CommonRestriction</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X83CB98F3783972DE" >1.3-3 ConcatenationProduct</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap1.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.html#X78B6216F7869E215" >1.4-1 IsHonest</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X806C879182E335B6" >1.4-2 HasFullDomain</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X7A5A03577DF86A1F" >1.4-3 HasFullCodomain</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X7B025572785DACBA" >1.4-4 IsSingleValued</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X85E05A137F6C759A" >1.4-5 IsTotal</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap1.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.html#X8276ADE97D53B8F0" >1.5-1 GeneralizedMorphismCategory</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X846BEA5784436575" >1.5-2 GeneralizedMorphismObject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X7F89465C80D5CB2F" >1.5-3 AsGeneralizedMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X7BCAEAEC78CE8093" >1.5-4 GeneralizedMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X87C5A2AC86D384BC" >1.5-5 GeneralizedMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X7DC1AF448411DFCE" >1.5-6 GeneralizedMorphismWithRangeAid</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X7D32834C7EA50379" >1.5-7 GeneralizedMorphismWithSourceAid</a></span >div ></div >div >div class="ContChap" ><a href="chap2.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.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.html#X8187BB8479575083" >2.1-1 IsGeneralizedMorphismCategoryByCospans</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X86C1877D7EC9F075" >2.1-2 IsGeneralizedMorphismCategoryByCospansObject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X82D8F9C38330F81E" >2.1-3 IsGeneralizedMorphismByCospan</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2.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.html#X815D6FE986CC3F99" >2.2-1 HasIdentityAsReversedArrow</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2.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.html#X7D7E0AB87D8C6BE4" >2.3-1 UnderlyingHonestObject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X7863825F85197D30" >2.3-2 Arrow</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X871D3BBC7E6B544B" >2.3-3 ReversedArrow</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X7DCA5A8278F4C569" >2.3-4 NormalizedCospanTuple</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X7F4AC0FE847140A4" >2.3-5 PseudoInverse</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X87E4921884F9F1FF" >2.3-6 GeneralizedInverseByCospan</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X7CFE9A12793AF805" >2.3-7 IdempotentDefinedBySubobjectByCospan</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X8330AB9480BC933A" >2.3-8 IdempotentDefinedByFactorobjectByCospan</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X7B636E0D7A9FA235" >2.3-9 NormalizedCospan</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2.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.html#X7988FD538374DC5C" >2.4-1 GeneralizedMorphismFromFactorToSubobjectByCospan</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2.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.html#X8313697F833CA064" >2.5-1 GeneralizedMorphismByCospan</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X865028F47CB5A9FA" >2.5-2 GeneralizedMorphismByCospan</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X7B744FE28475F25B" >2.5-3 GeneralizedMorphismByCospanWithSourceAid</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X79F31F9E80A5BFAD" >2.5-4 AsGeneralizedMorphismByCospan</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X879C3A4F82EC9C13" >2.5-5 GeneralizedMorphismCategoryByCospans</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X81ADB9C17D822C05" >2.5-6 GeneralizedMorphismByCospansObject</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2.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.html#X7A094900868E02F1" >2.6-1 AsGeneralizedMorphismByCospan</a></span >div ></div >div >div class="ContChap" ><a href="chap3.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.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.html#X7B3EA2C279A4F9E4" >3.1-1 IsGeneralizedMorphismCategoryBySpans</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X78F2B8E882ECF61E" >3.1-2 IsGeneralizedMorphismCategoryBySpansObject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X7A5BDCEE78549DFB" >3.1-3 IsGeneralizedMorphismBySpan</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3.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.html#X7A058F5C7F7116DB" >3.2-1 HasIdentityAsReversedArrow</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3.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.html#X7BDCF7FD7EAE01C3" >3.3-1 UnderlyingHonestObject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X83C847FC86AB508B" >3.3-2 Arrow</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X826CC0B57D6F7F3B" >3.3-3 ReversedArrow</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X8082EEE27FB449E5" >3.3-4 NormalizedSpanTuple</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X878EE24487756BD4" >3.3-5 PseudoInverse</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X800786037C19DEF5" >3.3-6 GeneralizedInverseBySpan</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X7B8C00217DD3A64C" >3.3-7 IdempotentDefinedBySubobjectBySpan</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X82D0B42E8413A5FE" >3.3-8 IdempotentDefinedByFactorobjectBySpan</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X86499E0D83A9D090" >3.3-9 NormalizedSpan</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3.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.html#X7D3675B0866191EC" >3.4-1 GeneralizedMorphismFromFactorToSubobjectBySpan</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3.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.html#X83FA5A4C787261DB" >3.5-1 GeneralizedMorphismBySpan</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X7EAF87447D2A08EE" >3.5-2 GeneralizedMorphismBySpan</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X79A8B50C7EB5ADE2" >3.5-3 GeneralizedMorphismBySpanWithRangeAid</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X79C48BB782BD799F" >3.5-4 AsGeneralizedMorphismBySpan</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X812CBF7580098CCF" >3.5-5 GeneralizedMorphismCategoryBySpans</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X817694F38145FD9F" >3.5-6 GeneralizedMorphismBySpansObject</a></span >div ></div >div >div class="ContChap" ><a href="chap4.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.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.html#X869A7C2A85C2743A" >4.1-1 IsGeneralizedMorphismCategoryByThreeArrows</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7E861596801CA565" >4.1-2 IsGeneralizedMorphismCategoryByThreeArrowsObject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X87934BAA84C6E654" >4.1-3 IsGeneralizedMorphismByThreeArrows</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4.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.html#X8247F41681D15233" >4.2-1 HasIdentitiesAsReversedArrows</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X8347A40179DBD909" >4.2-2 HasIdentityAsSourceAid</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X81F0F4FA78F9F361" >4.2-3 HasIdentityAsRangeAid</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4.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.html#X8028877F819A0DBF" >4.3-1 UnderlyingHonestObject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7B17B7587A449B8E" >4.3-2 SourceAid</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X87B0A0AF84F8AF7D" >4.3-3 RangeAid</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7CCBCD5385E55586" >4.3-4 Arrow</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X784C006B8525E205" >4.3-5 PseudoInverse</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X78A8A55883C06AB1" >4.3-6 GeneralizedInverseByThreeArrows</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X80E329707BAA3B29" >4.3-7 IdempotentDefinedBySubobjectByThreeArrows</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X8217014B870B3EC2" >4.3-8 IdempotentDefinedByFactorobjectByThreeArrows</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4.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.html#X78C1A22D86943E97" >4.4-1 GeneralizedMorphismFromFactorToSubobjectByThreeArrows</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7A50AC43855B33B1" >4.4-2 CommonCoastriction</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4.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.html#X8477D6E679E15474" >4.5-1 GeneralizedMorphismByThreeArrows</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7D60D9F97A2F7D5F" >4.5-2 GeneralizedMorphismByThreeArrowsWithSourceAid</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7F9E6B188755170A" >4.5-3 GeneralizedMorphismByThreeArrowsWithRangeAid</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7E0CF2A87AC08A8B" >4.5-4 AsGeneralizedMorphismByThreeArrows</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X8296606484DDDF6C" >4.5-5 GeneralizedMorphismCategoryByThreeArrows</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X8165802A8625467E" >4.5-6 GeneralizedMorphismByThreeArrowsObject</a></span >div ></div >div >div class="ContChap" ><a href="chap5.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.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.html#X79C6FF647D725997" >5.1-1 FunctorFromCospansToThreeArrows</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5.html#X8092A53484B9D89E" >5.1-2 FunctorFromCospansToSpans</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap5.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.html#X7A250CED7862BD61" >5.2-1 FunctorFromSpansToThreeArrows</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5.html#X80EAF5547D5E3A08" >5.2-2 FunctorFromSpansToCospans</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap5.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.html#X805E300E7CBA3F18" >5.3-1 FunctorFromThreeArrowsToCospans</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5.html#X7E0E745085802E80" >5.3-2 FunctorFromThreeArrowsToSpans</a></span >div ></div >div >div class="ContChap" ><a href="chap6.html#X877B8C39873C2938" >6 <span class="Heading" >Serre Quotients Subcategory</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap6.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.html#X7C2C5BC07CABE97D" >6.1-1 FullSubcategoryByMembershipFunction</a></span >div ></div >div >div class="ContChap" ><a href="chap7.html#X7E44E8FA8790C32A" >7 <span class="Heading" >Serre Quotients</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap7.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.html#X7BC5B052783425A2" >7.1-1 IsSerreQuotientCategoryObject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X82C2C3C27C0FC106" >7.1-2 IsSerreQuotientCategoryMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X8311C69E7FEEF417" >7.1-3 SerreQuotientCategory</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X7B2E75C3828CFEE4" >7.1-4 AsSerreQuotientCategoryObject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X8228022A7EB4CB66" >7.1-5 SerreQuotientCategoryMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X7C93747782930A14" >7.1-6 SerreQuotientCategoryMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X7FF1277C81BAD87E" >7.1-7 SerreQuotientCategoryMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X7BD12BC6873CB655" >7.1-8 SerreQuotientCategoryMorphismWithSourceAid</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X8461E2707FCF6EB0" >7.1-9 SerreQuotientCategoryMorphismWithRangeAid</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X7C2D68DA796082CE" >7.1-10 AsSerreQuotientCategoryMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X7F51A2A678518D91" >7.1-11 SubcategoryMembershipTestFunctionForSerreQuotient</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X8387D5C484A26089" >7.1-12 UnderlyingHonestCategory</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X7B0FD44F7FA4F8C1" >7.1-13 UnderlyingGeneralizedMorphismCategory</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X86E915208420C01C" >7.1-14 UnderlyingGeneralizedObject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X812EDC687898EEBF" >7.1-15 UnderlyingHonestObject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X7E403ABA78261622" >7.1-16 UnderlyingGeneralizedMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X7A1765BF783041DC" >7.1-17 CanonicalProjection</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap7.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.html#X7B0DFAB77891EB63" >7.2-1 SerreQuotientCategoryByCospans</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X7C696E9E83CA9250" >7.2-2 AsSerreQuotientCategoryByCospansObject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X7F1CBD4F82097FFE" >7.2-3 SerreQuotientCategoryByCospansMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X7B6DB3178122E617" >7.2-4 SerreQuotientCategoryByCospansMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X84649E8381E40A5E" >7.2-5 SerreQuotientCategoryByCospansMorphismWithSourceAid</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X8163B686820C8119" >7.2-6 SerreQuotientCategoryByCospansMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X83B53BAD85CDABE3" >7.2-7 AsSerreQuotientCategoryByCospansMorphism</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap7.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.html#X81B80C5882061F37" >7.3-1 SerreQuotientCategoryBySpans</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X82726E3C7A66996A" >7.3-2 AsSerreQuotientCategoryBySpansObject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X8540DCE084BB710F" >7.3-3 SerreQuotientCategoryBySpansMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X854E2C577EBC71A8" >7.3-4 SerreQuotientCategoryBySpansMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X85320AF0799B2ED6" >7.3-5 SerreQuotientCategoryBySpansMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X7BF244A67D0A7199" >7.3-6 SerreQuotientCategoryBySpansMorphismWithRangeAid</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X838E9D4D7BF0AA85" >7.3-7 AsSerreQuotientCategoryBySpansMorphism</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap7.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.html#X856C35F28411363D" >7.4-1 SerreQuotientCategoryByThreeArrows</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X80BDE2C9864D84B8" >7.4-2 AsSerreQuotientCategoryByThreeArrowsObject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X7E798D6882E5DBB4" >7.4-3 SerreQuotientCategoryByThreeArrowsMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X7AAB402C852E6030" >7.4-4 SerreQuotientCategoryByThreeArrowsMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X8597A92278BC8D63" >7.4-5 SerreQuotientCategoryByThreeArrowsMorphismWithSourceAid</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X820FF6B88188DB68" >7.4-6 SerreQuotientCategoryByThreeArrowsMorphismWithRangeAid</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X7DFC91D07E9A187B" >7.4-7 AsSerreQuotientCategoryByThreeArrowsMorphism</a></span >div ></div >div >div class="ContChap" ><a href="chap8.html#X79D7DBA7827EFB86" >8 <span class="Heading" >Serre Quotients Functors</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap8.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.html#X873A67F482BA7BFD" >8.1-1 SerreQuotientConversionFunctor</a></span >div ></div >div >div class="ContChap" ><a href="chap9.html#X7967FE8E7BBDF485" >9 <span class="Heading" >Examples and Tests</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap9.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.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.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.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.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.html#X7E8AFE5085FF7E15" >9.6 <span class="Heading" >IsWellDefined</span ></a>span >div >div >div class="ContChap" ><a href="chapInd.html" ><span class="Heading" >Index</span ></a></div >br />div >div class="chlinkprevnextbot" > <a href="chap0.html" >[Top of Book]</a> <a href="chap0.html#contents" 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