<?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 (ModulePresentationsForCAP) - 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="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 >ModulePresentationsForCAP</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 />br />Email: <span class="URL" ><a href="mailto:f.zickgraf@dashdos.com" >f.zickgraf@dashdos.com</a></span >br />Homepage: <span class="URL" ><a href="https://github.com/zickgraf/ " >https://github.com/zickgraf/</a></span >br />Address : <br />Walter-Flex-Str. 3<br /> 57068 Siegen<br /> Germany<br />"X8537FEB07AF2BEC8" name="X8537FEB07AF2BEC8" ></a></p>div class="contents" >"contents" name="contents" ></a></h3>div class="ContChap" ><a href="chap1.html#X7B8C95CA7DA733B4" >1 <span class="Heading" >Module Presentations</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap1.html#X78D1062D78BE08C1" >1.1 <span class="Heading" >Functors</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X7F7AC44478418555" >1.1-1 FunctorStandardModuleLeft</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X87AEC1177DB7F50D" >1.1-2 FunctorStandardModuleRight</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X8427C0B17A445822" >1.1-3 FunctorGetRidOfZeroGeneratorsLeft</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X7F1E779D8003146B" >1.1-4 FunctorGetRidOfZeroGeneratorsRight</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X819A04517B3601C0" >1.1-5 FunctorLessGeneratorsLeft</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X7F80AE9B7EC07198" >1.1-6 FunctorLessGeneratorsRight</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X877B7ACE87E1BEC2" >1.1-7 FunctorDualLeft</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X7D56611D7BF91B54" >1.1-8 FunctorDualRight</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X7C9901F8851FD24A" >1.1-9 FunctorDoubleDualLeft</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X8016306881444DCA" >1.1-10 FunctorDoubleDualRight</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap1.html#X7D03633A7D98026B" >1.2 <span class="Heading" >GAP Categories</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X79DBCB747E91FB70" >1.2-1 IsLeftOrRightPresentationMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X85E26CFF86855B6B" >1.2-2 IsLeftPresentationMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X873EFE29849F6998" >1.2-3 IsRightPresentationMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X7BB95B7A7EB96854" >1.2-4 IsLeftOrRightPresentation</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X7C71B8D17C60C6B5" >1.2-5 IsLeftPresentation</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X7DBF478D7EE3FE63" >1.2-6 IsRightPresentation</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap1.html#X86EC0F0A78ECBC10" >1.3 <span class="Heading" >Constructors</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X87010AB6819736C8" >1.3-1 PresentationMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X7C9B36AD7B9CCC8D" >1.3-2 AsMorphismBetweenFreeLeftPresentations</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X7F1AD55C852BE617" >1.3-3 AsMorphismBetweenFreeRightPresentations</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X7BE01A1381744627" >1.3-4 AsLeftPresentation</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X780443B07F43AA1C" >1.3-5 AsRightPresentation</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X7F345A2A87ABE417" >1.3-6 FreeLeftPresentation</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X85536E4E85D15252" >1.3-7 FreeRightPresentation</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X86F926B27C579E66" >1.3-8 UnderlyingMatrix</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X7D8E30E486A08439" >1.3-9 UnderlyingHomalgRing</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X7B5539AB8541F618" >1.3-10 Annihilator</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X87946F997AD1005A" >1.3-11 LeftPresentations</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X7BDF988F7FFEAB8C" >1.3-12 RightPresentations</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X8145816A85BA2680" >1.3-13 LeftPresentations_as_FreydCategory_CategoryOfRows</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X7ED9DFEB82DE9653" >1.3-14 RightPresentations_as_FreydCategory_CategoryOfColumns</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap1.html#X7C701DBF7BAE649A" >1.4 <span class="Heading" >Attributes</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X8157F3E8847B15E1" >1.4-1 UnderlyingHomalgRing</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X83CA6F06832162B7" >1.4-2 UnderlyingMatrix</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap1.html#X81CDBC6E7DBB4EA0" >1.5 <span class="Heading" >Non-Categorical Operations</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X8508310C7E908093" >1.5-1 StandardGeneratorMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X7EF1493A7D341F5E" >1.5-2 CoverByFreeModule</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap1.html#X836749D8814FEEE6" >1.6 <span class="Heading" >Natural Transformations</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X85D3DB1F856D05EF" >1.6-1 NaturalIsomorphismFromIdentityToStandardModuleLeft</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X7B64AF718133C945" >1.6-2 NaturalIsomorphismFromIdentityToStandardModuleRight</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X7CA2B84E7F933125" >1.6-3 NaturalIsomorphismFromIdentityToGetRidOfZeroGeneratorsLeft</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X7A2DCBD6844093E3" >1.6-4 NaturalIsomorphismFromIdentityToGetRidOfZeroGeneratorsRight</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X7B331B0A86010185" >1.6-5 NaturalIsomorphismFromIdentityToLessGeneratorsLeft</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X834AC0FD825FCD2F" >1.6-6 NaturalIsomorphismFromIdentityToLessGeneratorsRight</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X7E37CB058378CBEE" >1.6-7 NaturalTransformationFromIdentityToDoubleDualLeft</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X7F92B4448041A68C" >1.6-8 NaturalTransformationFromIdentityToDoubleDualRight</a></span >div ></div >div >div class="ContChap" ><a href="chap2.html#X7967FE8E7BBDF485" >2 <span class="Heading" >Examples and Tests</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2.html#X7FFB58F67850769C" >2.1 <span class="Heading" >Annihilator</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2.html#X86E8A9537A87B4EC" >2.2 <span class="Heading" >Intersection of Submodules</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2.html#X8296A25779A52244" >2.3 <span class="Heading" >Koszul Complex</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2.html#X808DC49C7ED99B52" >2.4 <span class="Heading" >Monoidal Categories</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2.html#X828DF9B1782D1AF6" >2.5 <span class="Heading" >Closed Monoidal Structure</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2.html#X7C3B1694803034A2" >2.6 <span class="Heading" >Projectivity test</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" >[Contents]</a> <a href="chap1.html" >[Next Chapter]</a> </div >div class="chlinkbot" ><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="chapInd.html" >Ind</a> </div >hr />"foot" >generated by <a href="https://www.math.rwth-aachen.de/~Frank.Luebeck/GAPDoc " >GAPDoc2HTML</a></p>body >html >quality 94%
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