<?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 >script type="text/javascript" "https://cdn.jsdelivr.net/npm/mathjax@2/MathJax.js?config=TeX-AMS-MML_HTMLorMML " >script >title >GAP (CAP) - Chapter 15: Terminal category</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="chap15" onload="jscontent()" >div class="chlinktop" ><span class="chlink1" >Goto Chapter: </span ><a href="chap0_mj.html" >Top</a> <a href="chap1_mj.html" >1</a> <a href="chap2_mj.html" >2</a> <a href="chap3_mj.html" >3</a> <a href="chap4_mj.html" >4</a> <a href="chap5_mj.html" >5</a> <a 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> </span ><a href="chap15_mj.html#X7D03633A7D98026B" >15.1 <span class="Heading" ><strong class="pkg" >GAP</strong > Categories</span span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap15_mj.html#X8665012E7D503742" >15.1-1 IsCapTerminalCategoryWithSingleObject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap15_mj.html#X7F48DB947BDA1232" >15.1-2 IsObjectInCapTerminalCategoryWithSingleObject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap15_mj.html#X86041A8F851354DB" >15.1-3 IsMorphismInCapTerminalCategoryWithSingleObject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap15_mj.html#X85A149A17E45806B" >15.1-4 IsCapTerminalCategoryWithMultipleObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap15_mj.html#X8751E72879CE707D" >15.1-5 IsObjectInCapTerminalCategoryWithMultipleObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap15_mj.html#X7BC47E5D7AD51588" >15.1-6 IsMorphismInCapTerminalCategoryWithMultipleObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap15_mj.html#X8724DDA281946BEB" >15.1-7 IsTerminalCategory</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap15_mj.html#X86EC0F0A78ECBC10" >15.2 <span class="Heading" >Constructors</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap15_mj.html#X7D7044AA82764329" >15.2-1 TerminalCategoryWithSingleObject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap15_mj.html#X7CBD1E9B81BBFFC8" >15.2-2 TerminalCategoryWithMultipleObjects</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap15_mj.html#X81FA767C792670A2" >15.2-3 CAP_INTERNAL_CONSTRUCTOR_FOR_TERMINAL_CATEGORY</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap15_mj.html#X7C701DBF7BAE649A" >15.3 <span class="Heading" >Attributes</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap15_mj.html#X7C2B3F018386B9D4" >15.3-1 TerminalCategoryWithSingleObjectUniqueObject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap15_mj.html#X87F66FAD7A1100C7" >15.3-2 TerminalCategoryWithSingleObjectUniqueMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap15_mj.html#X80813F9A86FCCC24" >15.3-3 FunctorFromTerminalCategory</a></span >div ></div >div >span class="Heading" >Terminal category</span ></h3>"X7D03633A7D98026B" name="X7D03633A7D98026B" ></a></p>span class="Heading" ><strong class="pkg" >GAP</strong > Categories</span ></h4>"X8665012E7D503742" name="X8665012E7D503742" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ IsCapTerminalCategoryWithSingleObject</code >( <var class="Arg" >T</var > )</td ><td class="tdright" >( filter )</td ></tr ></table ></div >code class="keyw" >true</code > or <code class="keyw" >false</code ></p>strong class="pkg" >GAP</strong > type of a terminal category with a single object .</p>"X7F48DB947BDA1232" name="X7F48DB947BDA1232" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ IsObjectInCapTerminalCategoryWithSingleObject</code >( <var class="Arg" >T</var > )</td ><td class="tdright" >( filter )</td ></tr ></table ></div >code class="keyw" >true</code > or <code class="keyw" >false</code ></p>strong class="pkg" >GAP</strong > type of an object in a terminal category with a single object .</p>"X86041A8F851354DB" name="X86041A8F851354DB" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ IsMorphismInCapTerminalCategoryWithSingleObject</code >( <var class="Arg" >T</var > )</td ><td class="tdright" >( filter )</td ></tr ></table ></div >code class="keyw" >true</code > or <code class="keyw" >false</code ></p>strong class="pkg" >GAP</strong > type of a morphism in a terminal category with a single object .</p>"X85A149A17E45806B" name="X85A149A17E45806B" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ IsCapTerminalCategoryWithMultipleObjects</code >( <var class="Arg" >T</var > )</td ><td class="tdright" >( filter )</td ></tr ></table ></div >code class="keyw" >true</code > or <code class="keyw" >false</code ></p>strong class="pkg" >GAP</strong > type of a terminal category with multiple objects.</p>"X8751E72879CE707D" name="X8751E72879CE707D" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ IsObjectInCapTerminalCategoryWithMultipleObjects</code >( <var class="Arg" >T</var > )</td ><td class="tdright" >( filter )</td ></tr ></table ></div >code class="keyw" >true</code > or <code class="keyw" >false</code ></p>strong class="pkg" >GAP</strong > type of an object in a terminal category with multiple objects.</p>"X7BC47E5D7AD51588" name="X7BC47E5D7AD51588" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ IsMorphismInCapTerminalCategoryWithMultipleObjects</code >( <var class="Arg" >T</var > )</td ><td class="tdright" >( filter )</td ></tr ></table ></div >code class="keyw" >true</code > or <code class="keyw" >false</code ></p>strong class="pkg" >GAP</strong > type of a morphism in a terminal category with multiple objects.</p>"X8724DDA281946BEB" name="X8724DDA281946BEB" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ IsTerminalCategory</code >( <var class="Arg" >C</var > )</td ><td class="tdright" >( property )</td ></tr ></table ></div >code class="keyw" >true</code > or <code class="keyw" >false</code ></p>var class="Arg" >C</var > being terminal.</p>"X86EC0F0A78ECBC10" name="X86EC0F0A78ECBC10" ></a></p>span class="Heading" >Constructors</span ></h4>"X7D7044AA82764329" name="X7D7044AA82764329" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ TerminalCategoryWithSingleObject</code >( <var class="Arg" >arg</var > )</td ><td class="tdright" >( function )</td ></tr ></table ></div >object .</p>"X7CBD1E9B81BBFFC8" name="X7CBD1E9B81BBFFC8" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ TerminalCategoryWithMultipleObjects</code >( <var class="Arg" >arg</var > )</td ><td class="tdright" >( function )</td ></tr ></table ></div >"X81FA767C792670A2" name="X81FA767C792670A2" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ CAP_INTERNAL_CONSTRUCTOR_FOR_TERMINAL_CATEGORY</code >( <var class="Arg" >options</var > )</td ><td class="tdright" >( function )</td ></tr ></table ></div >strong class="pkg" >CAP</strong > category</p>stments for TerminalCategoryWithSingleObject and TerminalCategoryWithMultipleObjects to the list of operations to install and the categorical properties of the given record, before passing it on to CategoryConstructor.</p>"X7C701DBF7BAE649A" name="X7C701DBF7BAE649A" ></a></p>span class="Heading" >Attributes</span ></h4>"X7C2B3F018386B9D4" name="X7C2B3F018386B9D4" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ TerminalCategoryWithSingleObjectUniqueObject</code >( <var class="Arg" >arg</var > )</td ><td class="tdright" td ></tr ></table ></div >strong class="pkg" >CAP</strong > object </p>object in a terminal category with a single object .</p>"X87F66FAD7A1100C7" name="X87F66FAD7A1100C7" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ TerminalCategoryWithSingleObjectUniqueMorphism</code >( <var class="Arg" >arg</var > )</td ><td class="tdright" >( attribute )</td ></tr ></table ></div >strong class="pkg" >CAP</strong > morphism</p>object .</p>"X80813F9A86FCCC24" name="X80813F9A86FCCC24" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ FunctorFromTerminalCategory</code >( <var class="Arg" >object </var > )</td ><td class="tdright" >( attribute )</td ></tr ></table ></div >strong class="pkg" >CAP</strong > functor</p>code class="code" >AsCapCategory( TerminalObject( CapCat ) )</code > mapping the unique object to <var class="Arg" >object </var >.</p>div class="chlinkprevnextbot" > <a href="chap0_mj.html" >[Top of Book]</a> <a href="chap0_mj.html#contents" >[Contents]</a> <a href="chap14_mj.html" >[Previous Chapter]</a> <a href="chap16_mj.html" >[Next Chapter]</a> </div >div 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