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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 basic functors.
####################################
#
# global variables:
#
####################################
####################################
#
# attributes:
#
####################################
## <#GAPDoc Label="CokernelEpi">
## <ManSection>
## <Attr Arg="phi" Name="CokernelEpi" Label="for morphisms"/>
## <Returns>a &homalg; morphism</Returns>
## <Description>
## The natural epimorphism from the <C>Range</C><M>(</M><A>phi</A><M>)</M>
## onto the <C>Cokernel</C><M>(</M><A>phi</A><M>)</M>.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "CokernelEpi",
IsHomalgMorphism );
## <#GAPDoc Label="CokernelNaturalGeneralizedIsomorphism">
## <ManSection>
## <Attr Arg="phi" Name="CokernelNaturalGeneralizedIsomorphism" Label="for morphisms"/>
## <Returns>a &homalg; morphism</Returns>
## <Description>
## The natural generalized isomorphism from the <C>Cokernel</C><M>(</M><A>phi</A><M>)</M>
## onto the <C>Range</C><M>(</M><A>phi</A><M>)</M>.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "CokernelNaturalGeneralizedIsomorphism",
IsHomalgMorphism );
## <#GAPDoc Label="KernelEmb">
## <ManSection>
## <Attr Arg="phi" Name="KernelEmb" Label="for morphisms"/>
## <Returns>a &homalg; morphism</Returns>
## <Description>
## The natural embedding of the <C>Kernel</C><M>(</M><A>phi</A><M>)</M>
## into the <C>Source</C><M>(</M><A>phi</A><M>)</M>.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "KernelEmb",
IsHomalgMorphism );
## <#GAPDoc Label="ImageObjectEmb">
## <ManSection>
## <Attr Arg="phi" Name="ImageObjectEmb" Label="for morphisms"/>
## <Returns>a &homalg; morphism</Returns>
## <Description>
## The natural embedding of the <C>ImageObject</C><M>(</M><A>phi</A><M>)</M>
## into the <C>Range</C><M>(</M><A>phi</A><M>)</M>.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "ImageObjectEmb",
IsHomalgMorphism );
## <#GAPDoc Label="ImageObjectEpi">
## <ManSection>
## <Attr Arg="phi" Name="ImageObjectEpi" Label="for morphisms"/>
## <Returns>a &homalg; morphism</Returns>
## <Description>
## The natural epimorphism from the <C>Source</C><M>(</M><A>phi</A><M>)</M>
## onto the <C>ImageObject</C><M>(</M><A>phi</A><M>)</M>.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "ImageObjectEpi",
IsHomalgMorphism );
## <#GAPDoc Label="NatTrIdToHomHom_R">
## <ManSection>
## <Attr Arg="M" Name="NatTrIdToHomHom_R" Label="for morphisms"/>
## <Returns>a &homalg; morphism</Returns>
## <Description>
## The natural evaluation morphism from the &homalg; object <A>M</A>
## to its double dual <C>HomHom</C><M>(</M><A>M</A><M>)</M>.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "NatTrIdToHomHom_R",
IsHomalgObject );
####################################
#
# global functions and operations:
#
####################################
# basic operations:
DeclareOperation( "Cokernel",
[ IsHomalgMorphism ] );
DeclareAttribute( "ImageObject",
IsHomalgMorphism );
## Kernel is already declared in the GAP library via DeclareOperation("Kernel",[IsObject]); (why so general?)
DeclareOperation( "DefectOfExactness",
[ IsHomalgComplex ] );
DeclareOperation( "DefectOfExactness",
[ IsHomalgMorphism, IsHomalgMorphism ] );
DeclareOperation( "Hom",
[ IsHomalgObject, IsHomalgObject ] );
DeclareOperation( "Ext",
[ IsInt, IsHomalgObject, IsHomalgObject ] );
DeclareOperation( "InternalHom",
[ IsHomalgObjectOrMorphism, IsHomalgObjectOrMorphism ] );
DeclareOperation( "InternalHom",
[ IsHomalgObjectOrMorphism ] );
DeclareOperation( "InternalExt",
[ IsInt, IsHomalgObjectOrMorphism, IsHomalgObjectOrMorphism ] );
DeclareOperation( "InternalExt",
[ IsHomalgObjectOrMorphism, IsHomalgObjectOrMorphism ] );
DeclareOperation( "InternalExt",
[ IsInt, IsHomalgObjectOrMorphism ] );
DeclareOperation( "InternalExt",
[ IsHomalgObjectOrMorphism ] );
DeclareOperation( "Tor",
[ IsInt, IsHomalgObject, IsHomalgObject ] );
DeclareOperation( "LeftDualizingFunctor",
[ IsStructureObject, IsString ] );
DeclareOperation( "LeftDualizingFunctor",
[ IsStructureObject ] );
DeclareOperation( "RightDualizingFunctor",
[ IsStructureObject, IsString ] );
DeclareOperation( "RightDualizingFunctor",
[ IsStructureObject ] );
DeclareOperation( "Dualize",
[ IsStructureObjectOrObjectOrMorphism ] );
DeclareOperation( "TensorProductOp",
[ IsList, IsStructureObjectOrObjectOrMorphism ] );
DeclareOperation( "BaseChange",
[ IsStructureObject, IsHomalgStaticObject ] );
####################################
#
# synonyms:
#
####################################
DeclareSynonym( "DefectOfHoms",
DefectOfExactness );
[ Dauer der Verarbeitung: 0.18 Sekunden
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