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# SPDX-License-Identifier: GPL-2.0-or-later
# homalg: A homological algebra meta-package for computable Abelian categories
#
# Declarations
#
## Declarations for functors.
####################################
#
# categories:
#
####################################
# A new GAP-category:
## <#GAPDoc Label="IsHomalgFunctor">
## <ManSection>
## <Filt Type="Category" Arg="F" Name="IsHomalgFunctor"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## The &GAP; category of &homalg; (multi-)functors.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareCategory( "IsHomalgFunctor",
IsAttributeStoringRep );
####################################
#
# properties:
#
####################################
####################################
#
# attributes:
#
####################################
## <#GAPDoc Label="NameOfFunctor">
## <ManSection>
## <Attr Arg="F" Name="NameOfFunctor"/>
## <Returns>a string</Returns>
## <Description>
## The name of the &homalg; functor <A>F</A>.
## <Example><![CDATA[
## gap> NameOfFunctor( Functor_Ext_for_fp_modules );
## "Ext"
## gap> Display( Functor_Ext_for_fp_modules );
## Ext
## ]]></Example>
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "NameOfFunctor",
IsHomalgFunctor );
## <#GAPDoc Label="OperationOfFunctor">
## <ManSection>
## <Attr Arg="F" Name="OperationOfFunctor"/>
## <Returns>an operation</Returns>
## <Description>
## The operation of the functor <A>F</A>.
## <Example><![CDATA[
## gap> Functor_Ext_for_fp_modules;
## <The functor Ext for f.p. modules and their maps over computable rings>
## gap> OperationOfFunctor( Functor_Ext_for_fp_modules );
## <Operation "Ext">
## ]]></Example>
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "OperationOfFunctor",
IsHomalgFunctor );
## <#GAPDoc Label="Genesis:functor">
## <ManSection>
## <Attr Arg="F" Name="Genesis"/>
## <Returns>a list</Returns>
## <Description>
## The first entry of the returned list is the name of the constructor used to create the functor <A>F</A>.
## The reset of the list contains arguments that were passed to this constructor for creating <A>F</A>.
## <P/>
## These are examples of different functors created using the different constructors:
## <List>
## <Item> <C>CreateHomalgFunctor</C>:
## <Example><![CDATA[
## gap> Functor_Hom_for_fp_modules;
## <The functor Hom for f.p. modules and their maps over computable rings>
## ]]></Example></Item>
## <Item> <C>InsertObjectInMultiFunctor</C>:
## <Example><![CDATA[
## gap> zz := HomalgRingOfIntegers( );
## Z
## gap> LeftDualizingFunctor( zz, "ZZ_Hom" );
## <The functor ZZ_Hom for f.p. modules and their maps over computable rings>
## gap> Functor_ZZ_Hom_for_fp_modules; ## got automatically defined
## <The functor ZZ_Hom for f.p. modules and their maps over computable rings>
## gap> ZZ_Hom; ## got automatically defined
## <Operation "ZZ_Hom">
## gap> Genesis( Functor_ZZ_Hom_for_fp_modules );
## [ "InsertObjectInMultiFunctor",
## <The functor Hom for f.p. modules and their maps over computable rings>, 2,
## <The free left module of rank 1 on a free generator> ]
## gap> 1 * zz;
## <The free left module of rank 1 on a free generator>
## ]]></Example></Item>
## <Item> <C>LeftDerivedFunctor</C>:
## <Example><![CDATA[
## gap> Functor_TensorProduct_for_fp_modules;
## <The functor TensorProduct for f.p. modules and their maps over computable rin\
## gs>
## gap> Genesis( Functor_LTensorProduct_for_fp_modules );
## [ "LeftDerivedFunctor",
## <The functor TensorProduct for f.p. modules and their maps over computable r\
## ings>, 1 ]
## ]]></Example></Item>
## <Item> <C>RightDerivedCofunctor</C>:
## <Example><![CDATA[
## gap> Genesis( Functor_RHom_for_fp_modules );
## [ "RightDerivedCofunctor",
## <The functor Hom for f.p. modules and their maps over computable rings>, 1 ]
## ]]></Example></Item>
## <Item> <C>LeftSatelliteOfFunctor</C>:
## <Example><![CDATA[
## gap> Genesis( Functor_Tor_for_fp_modules );
## [ "LeftSatelliteOfFunctor",
## <The functor TensorProduct for f.p. modules and their maps over computable r\
## ings>, 1 ]
## ]]></Example></Item>
## <Item> <C>RightSatelliteOfCofunctor</C>:
## <Example><![CDATA[
## gap> Genesis( Functor_Ext_for_fp_modules );
## [ "RightSatelliteOfCofunctor",
## <The functor Hom for f.p. modules and their maps over computable rings>, 1 ]
## ]]></Example></Item>
## <Item> <C>ComposeFunctors</C>:
## <Example><![CDATA[
## gap> Genesis( Functor_HomHom_for_fp_modules );
## [ "ComposeFunctors",
## [ <The functor Hom for f.p. modules and their maps over computable rings>,
## <The functor Hom for f.p. modules and their maps over computable rings>
## ], 1 ]
## gap> ValueGlobal( "ComposeFunctors" );
## <Operation "ComposeFunctors">
## ]]></Example></Item>
## </List>
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "Genesis",
IsHomalgFunctor, "mutable" );
## <#GAPDoc Label="ProcedureToReadjustGenerators:functor">
## <ManSection>
## <Attr Arg="Functor" Name="ProcedureToReadjustGenerators" Label="for functors"/>
## <Returns>a function</Returns>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "ProcedureToReadjustGenerators",
IsHomalgFunctor );
####################################
#
# global functions and operations:
#
####################################
# constructors:
DeclareGlobalFunction( "CreateHomalgFunctor" );
DeclareOperation( "CategoryOfFunctor",
[ IsHomalgFunctor ] );
DeclareOperation( "DescriptionOfCategory",
[ IsHomalgFunctor ] );
DeclareOperation( "ShortDescriptionOfCategory",
[ IsHomalgFunctor ] );
DeclareOperation( "InsertObjectInMultiFunctor",
[ IsHomalgFunctor, IsInt, IsStructureObjectOrObjectOrMorphism, IsString, IsString ] );
DeclareOperation( "InsertObjectInMultiFunctor",
[ IsHomalgFunctor, IsInt, IsStructureObjectOrObjectOrMorphism, IsString ] );
DeclareOperation( "ComposeFunctors",
[ IsHomalgFunctor, IsInt, IsHomalgFunctor, IsString, IsString ] );
DeclareOperation( "ComposeFunctors",
[ IsHomalgFunctor, IsInt, IsHomalgFunctor, IsString ] );
DeclareOperation( "ComposeFunctors",
[ IsHomalgFunctor, IsInt, IsHomalgFunctor ] );
DeclareOperation( "ComposeFunctors",
[ IsHomalgFunctor, IsHomalgFunctor, IsString, IsString ] );
DeclareOperation( "ComposeFunctors",
[ IsHomalgFunctor, IsHomalgFunctor, IsString ] );
DeclareOperation( "ComposeFunctors",
[ IsHomalgFunctor, IsHomalgFunctor ] );
DeclareOperation( "*",
[ IsHomalgFunctor, IsHomalgFunctor ] );
DeclareOperation( "RightSatelliteOfCofunctor",
[ IsHomalgFunctor, IsInt, IsString, IsString ] );
DeclareOperation( "RightSatelliteOfCofunctor",
[ IsHomalgFunctor, IsInt, IsString ] );
DeclareOperation( "RightSatelliteOfCofunctor",
[ IsHomalgFunctor, IsInt ] );
DeclareOperation( "RightSatelliteOfCofunctor",
[ IsHomalgFunctor, IsString, IsString ] );
DeclareOperation( "RightSatelliteOfCofunctor",
[ IsHomalgFunctor, IsString ] );
DeclareOperation( "RightSatelliteOfCofunctor",
[ IsHomalgFunctor ] );
DeclareOperation( "LeftSatelliteOfFunctor",
[ IsHomalgFunctor, IsInt, IsString, IsString ] );
DeclareOperation( "LeftSatelliteOfFunctor",
[ IsHomalgFunctor, IsInt, IsString ] );
DeclareOperation( "LeftSatelliteOfFunctor",
[ IsHomalgFunctor, IsInt ] );
DeclareOperation( "LeftSatelliteOfFunctor",
[ IsHomalgFunctor, IsString, IsString ] );
DeclareOperation( "LeftSatelliteOfFunctor",
[ IsHomalgFunctor, IsString ] );
DeclareOperation( "LeftSatelliteOfFunctor",
[ IsHomalgFunctor ] );
DeclareOperation( "RightDerivedCofunctor",
[ IsHomalgFunctor, IsInt, IsString, IsString ] );
DeclareOperation( "RightDerivedCofunctor",
[ IsHomalgFunctor, IsInt, IsString ] );
DeclareOperation( "RightDerivedCofunctor",
[ IsHomalgFunctor, IsInt ] );
DeclareOperation( "RightDerivedCofunctor",
[ IsHomalgFunctor, IsString, IsString ] );
DeclareOperation( "RightDerivedCofunctor",
[ IsHomalgFunctor, IsString ] );
DeclareOperation( "RightDerivedCofunctor",
[ IsHomalgFunctor ] );
DeclareOperation( "LeftDerivedFunctor",
[ IsHomalgFunctor, IsInt, IsString, IsString ] );
DeclareOperation( "LeftDerivedFunctor",
[ IsHomalgFunctor, IsInt, IsString ] );
DeclareOperation( "LeftDerivedFunctor",
[ IsHomalgFunctor, IsInt ] );
DeclareOperation( "LeftDerivedFunctor",
[ IsHomalgFunctor, IsString, IsString ] );
DeclareOperation( "LeftDerivedFunctor",
[ IsHomalgFunctor, IsString ] );
DeclareOperation( "LeftDerivedFunctor",
[ IsHomalgFunctor ] );
# basic operations:
DeclareOperation( "NaturalGeneralizedEmbedding",
[ IsHomalgStaticObject ] );
DeclareOperation( "IsSpecialFunctor",
[ IsHomalgFunctor ] );
DeclareOperation( "MultiplicityOfFunctor",
[ IsHomalgFunctor ] );
DeclareOperation( "IsCovariantFunctor",
[ IsHomalgFunctor, IsInt ] );
DeclareOperation( "IsCovariantFunctor",
[ IsHomalgFunctor ] );
DeclareOperation( "IsDistinguishedArgumentOfFunctor",
[ IsHomalgFunctor, IsInt ] );
DeclareOperation( "IsDistinguishedFirstArgumentOfFunctor",
[ IsHomalgFunctor ] );
DeclareOperation( "IsAdditiveFunctor",
[ IsHomalgFunctor, IsInt ] );
DeclareOperation( "IsAdditiveFunctor",
[ IsHomalgFunctor ] );
DeclareOperation( "IsLeftExactFunctor",
[ IsHomalgFunctor, IsInt ] );
DeclareOperation( "IsLeftExactFunctor",
[ IsHomalgFunctor ] );
DeclareOperation( "IsRightExactFunctor",
[ IsHomalgFunctor, IsInt ] );
DeclareOperation( "IsRightExactFunctor",
[ IsHomalgFunctor ] );
DeclareOperation( "IsIdenticalObjForFunctors",
[ IsObject, IsObject ] );
DeclareOperation( "GetContainerForWeakPointersOfFunctorCachedValue",
[ IsHomalgFunctor, IsHomalgCategory, IsString ] );
DeclareOperation( "SetFunctorObjCachedValue",
[ IsHomalgFunctor, IsList, IsObject ] );
DeclareOperation( "GetFunctorObjCachedValue",
[ IsHomalgFunctor, IsList ] );
DeclareOperation( "FunctorObj",
[ IsHomalgFunctor, IsList ] );
DeclareOperation( "FunctorMor",
[ IsHomalgFunctor, IsHomalgMorphism, IsList ] );
DeclareOperation( "FunctorMor",
[ IsHomalgFunctor, IsHomalgMorphism ] );
DeclareOperation( "SetPropertiesOfFunctorMor",
[ IsHomalgFunctor, IsHomalgMorphism, IsHomalgMorphism, IsInt, IsList, IsList ] );
DeclareOperation( "InstallFunctorOnObjects",
[ IsHomalgFunctor ] );
DeclareOperation( "InstallNaturalTransformationsOfFunctor",
[ IsHomalgFunctor ] );
DeclareOperation( "SetNaturalTransformation",
[ IsHomalgFunctor, IsList, IsString, IsObject ] );
DeclareOperation( "InstallFunctorOnMorphisms",
[ IsHomalgFunctor ] );
DeclareOperation( "InstallSpecialFunctorOnMorphisms",
[ IsHomalgFunctor ] );
DeclareOperation( "InstallFunctorOnComplexes",
[ IsHomalgFunctor ] );
DeclareOperation( "InstallFunctorOnChainMorphisms",
[ IsHomalgFunctor ] );
DeclareOperation( "InstallFunctor",
[ IsHomalgFunctor ] );
DeclareOperation( "InstallDeltaFunctor",
[ IsHomalgFunctor ] );
DeclareGlobalFunction( "HelperToInstallUnivariateFunctorOnComplexes" );
DeclareGlobalFunction( "HelperToInstallFirstArgumentOfBivariateFunctorOnComplexes" );
DeclareGlobalFunction( "HelperToInstallSecondArgumentOfBivariateFunctorOnComplexes" );
DeclareGlobalFunction( "HelperToInstallFirstArgumentOfBivariateFunctorOnMorphismsAndSecondArgumentOnComplexes" );
DeclareGlobalFunction( "HelperToInstallFirstAndSecondArgumentOfBivariateFunctorOnComplexes" );
DeclareGlobalFunction( "HelperToInstallUnivariateFunctorOnChainMorphisms" );
DeclareGlobalFunction( "HelperToInstallFirstArgumentOfBivariateFunctorOnChainMorphisms" );
DeclareGlobalFunction( "HelperToInstallSecondArgumentOfBivariateFunctorOnChainMorphisms" );
DeclareGlobalFunction( "HelperToInstallUnivariateDeltaFunctor" );
DeclareGlobalFunction( "HelperToInstallFirstArgumentOfBivariateDeltaFunctor" );
DeclareGlobalFunction( "HelperToInstallSecondArgumentOfBivariateDeltaFunctor" );
DeclareGlobalFunction( "HelperToInstallFirstArgumentOfTrivariateDeltaFunctor" );
DeclareGlobalFunction( "HelperToInstallSecondArgumentOfTrivariateDeltaFunctor" );
DeclareGlobalFunction( "HelperToInstallThirdArgumentOfTrivariateDeltaFunctor" );
DeclareGlobalFunction( "CallOperationFromCategory" );
[ Dauer der Verarbeitung: 0.4 Sekunden
(vorverarbeitet)
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