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products/Sources/formale Sprachen/GAP/pkg/cap/doc/ (Algebra von RWTH Aachen Version 4.15.1^©) Datei vom 22.8.2025 mit Größe 4 kB

Quelle _Chapter_Terminal_category.xml Sprache: XML

<?xml version="1.0" encoding="UTF-8"?>


<Chapter Label="Chapter_Terminal_category">
<Heading>Terminal category</Heading>

<P/>
<Section Label="Chapter_Terminal_category_Section_GAP_Categories">
<Heading>&GAP; Categories</Heading>

<ManSection>
  <Filt Arg="T" Name="IsCapTerminalCategoryWithSingleObject" Label="for IsCapCategory"/>
<Returns><K>true</K> or <K>false</K>
</Returns>
<Description>
  The &GAP; type of a terminal category with a single object.
</Description>
</ManSection>

<ManSection>
  <Filt Arg="T" Name="IsObjectInCapTerminalCategoryWithSingleObject" Label="for IsCapCategoryObject"/>
<Returns><K>true</K> or <K>false</K>
</Returns>
<Description>
  The &GAP; type of an object in a terminal category with a single object.
</Description>
</ManSection>

<ManSection>
  <Filt Arg="T" Name="IsMorphismInCapTerminalCategoryWithSingleObject" Label="for IsCapCategoryMorphism"/>
<Returns><K>true</K> or <K>false</K>
</Returns>
<Description>
  The &GAP; type of a morphism in a terminal category with a single object.
</Description>
</ManSection>

<ManSection>
  <Filt Arg="T" Name="IsCapTerminalCategoryWithMultipleObjects" Label="for IsCapCategory"/>
<Returns><K>true</K> or <K>false</K>
</Returns>
<Description>
  The &GAP; type of a terminal category with multiple objects.
</Description>
</ManSection>

<ManSection>
  <Filt Arg="T" Name="IsObjectInCapTerminalCategoryWithMultipleObjects" Label="for IsCapCategoryObject"/>
<Returns><K>true</K> or <K>false</K>
</Returns>
<Description>
  The &GAP; type of an object in a terminal category with multiple objects.
</Description>
</ManSection>

<ManSection>
  <Filt Arg="T" Name="IsMorphismInCapTerminalCategoryWithMultipleObjects" Label="for IsCapCategoryMorphism"/>
<Returns><K>true</K> or <K>false</K>
</Returns>
<Description>
  The &GAP; type of a morphism in a terminal category with multiple objects.
</Description>
</ManSection>

<ManSection>
  <Prop Arg="C" Name="IsTerminalCategory" Label="for IsCapCategory"/>
<Returns><K>true</K> or <K>false</K>
</Returns>
<Description>
  The property of the category <A>C</A> being terminal.
</Description>
</ManSection>

</Section>

<Section Label="Chapter_Terminal_category_Section_Constructors">
<Heading>Constructors</Heading>

<ManSection>
  <Func Arg="arg" Name="TerminalCategoryWithSingleObject" />
<Description>
  Construct a terminal category with a single object.
</Description>
</ManSection>

<ManSection>
  <Func Arg="arg" Name="TerminalCategoryWithMultipleObjects" />
<Description>
  Construct a terminal category with multiple objects.
</Description>
</ManSection>

<ManSection>
  <Func Arg="options" Name="CAP_INTERNAL_CONSTRUCTOR_FOR_TERMINAL_CATEGORY" />
<Returns>a &CAP; category
</Returns>
<Description>
  This function takes a record of options suited for CategoryConstructor.
  It makes common adjustments 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.
</Description>
</ManSection>

</Section>

<Section Label="Chapter_Terminal_category_Section_Attributes">
<Heading>Attributes</Heading>

<ManSection>
  <Attr Arg="arg" Name="TerminalCategoryWithSingleObjectUniqueObject" Label="for IsCapTerminalCategoryWithSingleObject"/>
<Returns>a &CAP; object
</Returns>
<Description>
  The unique object in a terminal category with a single object.
</Description>
</ManSection>

<ManSection>
  <Attr Arg="arg" Name="TerminalCategoryWithSingleObjectUniqueMorphism" Label="for IsCapTerminalCategoryWithSingleObject"/>
<Returns>a &CAP; morphism
</Returns>
<Description>
  The unique morphism in a terminal category with a single object.
</Description>
</ManSection>

<ManSection>
  <Attr Arg="object" Name="FunctorFromTerminalCategory" Label="for IsCapCategoryObject"/>
<Returns>a &CAP; functor
</Returns>
<Description>
  A functor from <Code>AsCapCategory( TerminalObject( CapCat ) )</Code> mapping the unique object to <A>object</A>.
</Description>
</ManSection>

</Section>

</Chapter>

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