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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 homalg bigraded objects.
####################################
#
# categories:
#
####################################
# a new GAP-category:
## <#GAPDoc Label="IsHomalgBigradedObject">
## <ManSection>
## <Filt Type="Category" Arg="Er" Name="IsHomalgBigradedObject"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## The &GAP; category of &homalg; bigraded objects. <P/>
## (It is a subcategory of the &GAP; category <C>IsHomalgObject</C>.)
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareCategory( "IsHomalgBigradedObject",
IsHomalgObject );
# three new GAP-subcategories:
## <#GAPDoc Label="IsHomalgBigradedObjectAssociatedToAnExactCouple">
## <ManSection>
## <Filt Type="Category" Arg="Er" Name="IsHomalgBigradedObjectAssociatedToAnExactCouple"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## The &GAP; category of &homalg; bigraded objects associated to an exact couple. <P/>
## (It is a subcategory of the &GAP; category <C>IsHomalgBigradedObject</C>.)
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareCategory( "IsHomalgBigradedObjectAssociatedToAnExactCouple",
IsHomalgBigradedObject );
## <#GAPDoc Label="IsHomalgBigradedObjectAssociatedToAFilteredComplex">
## <ManSection>
## <Filt Type="Category" Arg="Er" Name="IsHomalgBigradedObjectAssociatedToAFilteredComplex"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## The &GAP; category of &homalg; bigraded objects associated to a filtered complex. <Br/>
## The <M>0</M>-th spectral sheet <M>E_0</M> stemming from a filtration is a bigraded (differential) object,
## which, in general, does not stem from an exact couple (although <M>E_1</M>, <M>E_2</M>, ... do). <P/>
## (It is a subcategory of the &GAP; category <C>IsHomalgBigradedObject</C>.)
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareCategory( "IsHomalgBigradedObjectAssociatedToAFilteredComplex",
IsHomalgBigradedObject );
## <#GAPDoc Label="IsHomalgBigradedObjectAssociatedToABicomplex">
## <ManSection>
## <Filt Type="Category" Arg="Er" Name="IsHomalgBigradedObjectAssociatedToABicomplex"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## The &GAP; category of &homalg; bigraded objects associated to a bicmplex. <P/>
## (It is a subcategory of the &GAP; category <Br/>
## <C>IsHomalgBigradedObjectAssociatedToAFilteredComplex</C>.)
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareCategory( "IsHomalgBigradedObjectAssociatedToABicomplex",
IsHomalgBigradedObjectAssociatedToAFilteredComplex );
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#
# properties:
#
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## <#GAPDoc Label="IsEndowedWithDifferential">
## <ManSection>
## <Prop Arg="Er" Name="IsEndowedWithDifferential"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## Check if <A>Er</A> is a differential bigraded object. <Br/>
## (no method installed)
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "IsEndowedWithDifferential",
IsHomalgBigradedObject );
## <#GAPDoc Label="IsStableSheet">
## <ManSection>
## <Prop Arg="Er" Name="IsStableSheet"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## Check if <A>Er</A> is stable. <Br/>
## (no method installed)
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "IsStableSheet",
IsHomalgBigradedObject );
####################################
#
# global functions and operations:
#
####################################
# constructors:
DeclareOperation( "HomalgBigradedObject",
[ IsHomalgBicomplex ] );
DeclareOperation( "AsDifferentialObject",
[ IsHomalgBigradedObject ] );
DeclareOperation( "DefectOfExactness",
[ IsHomalgBigradedObject ] );
# basic operations:
DeclareOperation( "ObjectDegreesOfBigradedObject",
[ IsHomalgBigradedObject ] );
DeclareOperation( "CertainObject",
[ IsHomalgBigradedObject, IsList ] );
DeclareOperation( "ObjectsOfBigradedObject",
[ IsHomalgBigradedObject ] );
DeclareOperation( "LowestBidegreeInBigradedObject",
[ IsHomalgBigradedObject ] );
DeclareOperation( "HighestBidegreeInBigradedObject",
[ IsHomalgBigradedObject ] );
DeclareOperation( "LowestBidegreeObjectInBigradedObject",
[ IsHomalgBigradedObject ] );
DeclareOperation( "HighestBidegreeObjectInBigradedObject",
[ IsHomalgBigradedObject ] );
DeclareOperation( "CertainMorphism",
[ IsHomalgBigradedObject, IsList ] );
DeclareOperation( "UnderlyingBicomplex",
[ IsHomalgBigradedObjectAssociatedToABicomplex ] );
DeclareOperation( "BidegreeOfDifferential",
[ IsHomalgBigradedObject ] );
DeclareOperation( "LevelOfBigradedObject",
[ IsHomalgBigradedObject ] );
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