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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 spectral sequences.
####################################
#
# categories:
#
####################################
# a new GAP-category:
## <#GAPDoc Label="IsHomalgSpectralSequence">
## <ManSection>
## <Filt Type="Category" Arg="E" Name="IsHomalgSpectralSequence"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## The &GAP; category of &homalg; (co)homological spectral sequences. <P/>
## (It is a subcategory of the &GAP; category <C>IsHomalgObject</C>.)
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareCategory( "IsHomalgSpectralSequence",
IsHomalgObject );
# three new GAP-subcategories:
## <#GAPDoc Label="IsHomalgSpectralSequenceAssociatedToAnExactCouple">
## <ManSection>
## <Filt Type="Category" Arg="E" Name="IsHomalgSpectralSequenceAssociatedToAnExactCouple"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## The &GAP; category of &homalg; associated to an exact couple. <P/>
## (It is a subcategory of the &GAP; category <C>IsHomalgSpectralSequence</C>.)
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareCategory( "IsHomalgSpectralSequenceAssociatedToAnExactCouple",
IsHomalgSpectralSequence );
## <#GAPDoc Label="IsHomalgSpectralSequenceAssociatedToAFilteredComplex">
## <ManSection>
## <Filt Type="Category" Arg="E" Name="IsHomalgSpectralSequenceAssociatedToAFilteredComplex"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## The &GAP; category of &homalg; associated to a filtered complex. <P/>
## (It is a subcategory of the &GAP; category <C>IsHomalgSpectralSequence</C>.) <Br/><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).
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareCategory( "IsHomalgSpectralSequenceAssociatedToAFilteredComplex",
IsHomalgSpectralSequence );
## <#GAPDoc Label="IsHomalgSpectralSequenceAssociatedToABicomplex">
## <ManSection>
## <Filt Type="Category" Arg="E" Name="IsHomalgSpectralSequenceAssociatedToABicomplex"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## The &GAP; category of &homalg; associated to a bicomplex. <P/>
## (It is a subcategory of the &GAP; category <Br/>
## <C>IsHomalgSpectralSequenceAssociatedToAFilteredComplex</C>.)
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareCategory( "IsHomalgSpectralSequenceAssociatedToABicomplex",
IsHomalgSpectralSequenceAssociatedToAFilteredComplex );
####################################
#
# attributes:
#
####################################
## <#GAPDoc Label="GeneralizedEmbeddingsInTotalObjects">
## <ManSection>
## <Attr Arg="E" Name="GeneralizedEmbeddingsInTotalObjects"/>
## <Returns>a record containing &homalg; maps</Returns>
## <Description>
## The generalized embbedings of the objects in the stable sheet into the objects of the associated total complex.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "GeneralizedEmbeddingsInTotalObjects",
IsHomalgSpectralSequence );
## <#GAPDoc Label="GeneralizedEmbeddingsInTotalDefects">
## <ManSection>
## <Attr Arg="E" Name="GeneralizedEmbeddingsInTotalDefects"/>
## <Returns>a record containing &homalg; maps</Returns>
## <Description>
## The generalized embbedings of the objects in the stable sheet into the defects of the associated total complex.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "GeneralizedEmbeddingsInTotalDefects",
IsHomalgSpectralSequence );
####################################
#
# global functions and operations:
#
####################################
# constructors:
DeclareOperation( "HomalgSpectralSequence",
[ IsInt, IsHomalgBicomplex, IsInt ] );
DeclareOperation( "HomalgSpectralSequence",
[ IsInt, IsHomalgBicomplex ] );
DeclareOperation( "HomalgSpectralSequence",
[ IsHomalgBicomplex, IsInt ] );
DeclareOperation( "HomalgSpectralSequence",
[ IsHomalgBicomplex ] );
# basic operations:
DeclareOperation( "LevelsOfSpectralSequence",
[ IsHomalgSpectralSequence ] );
DeclareOperation( "CertainSheet",
[ IsHomalgSpectralSequence, IsInt ] );
DeclareOperation( "LowestLevelInSpectralSequence",
[ IsHomalgSpectralSequence ] );
DeclareOperation( "HighestLevelInSpectralSequence",
[ IsHomalgSpectralSequence ] );
DeclareOperation( "SheetsOfSpectralSequence",
[ IsHomalgSpectralSequence ] );
DeclareOperation( "LowestLevelSheetInSpectralSequence",
[ IsHomalgSpectralSequence ] );
DeclareOperation( "HighestLevelSheetInSpectralSequence",
[ IsHomalgSpectralSequence ] );
DeclareOperation( "ObjectDegreesOfSpectralSequence",
[ IsHomalgSpectralSequence ] );
DeclareOperation( "CertainObject",
[ IsHomalgSpectralSequence, IsList, IsInt ] );
DeclareOperation( "CertainObject",
[ IsHomalgSpectralSequence, IsList ] );
DeclareOperation( "ObjectsOfSpectralSequence",
[ IsHomalgSpectralSequence, IsInt ] );
DeclareOperation( "ObjectsOfSpectralSequence",
[ IsHomalgSpectralSequence ] );
DeclareOperation( "LowestBidegreeInSpectralSequence",
[ IsHomalgSpectralSequence ] );
DeclareOperation( "HighestBidegreeInSpectralSequence",
[ IsHomalgSpectralSequence ] );
DeclareOperation( "LowestTotalDegreeInSpectralSequence",
[ IsHomalgSpectralSequence ] );
DeclareOperation( "HighestTotalDegreeInSpectralSequence",
[ IsHomalgSpectralSequence ] );
DeclareOperation( "TotalDegreesOfSpectralSequence",
[ IsHomalgSpectralSequence ] );
DeclareOperation( "BidegreesOfSpectralSequence",
[ IsHomalgSpectralSequence, IsInt ] );
DeclareOperation( "LowestBidegreeObjectInSpectralSequence",
[ IsHomalgSpectralSequence, IsInt ] );
DeclareOperation( "LowestBidegreeObjectInSpectralSequence",
[ IsHomalgSpectralSequence ] );
DeclareOperation( "HighestBidegreeObjectInSpectralSequence",
[ IsHomalgSpectralSequence, IsInt ] );
DeclareOperation( "HighestBidegreeObjectInSpectralSequence",
[ IsHomalgSpectralSequence ] );
DeclareOperation( "CertainMorphism",
[ IsHomalgSpectralSequence, IsList, IsInt ] );
DeclareOperation( "CertainMorphism",
[ IsHomalgSpectralSequence, IsList ] );
DeclareOperation( "UnderlyingBicomplex",
[ IsHomalgSpectralSequenceAssociatedToABicomplex ] );
DeclareOperation( "AssociatedFilteredComplex",
[ IsHomalgSpectralSequence ] );
DeclareOperation( "AssociatedFirstSpectralSequence",
[ IsHomalgSpectralSequence ] );
DeclareOperation( "LevelOfStability",
[ IsHomalgSpectralSequence, IsList, IsInt ] );
DeclareOperation( "LevelOfStability",
[ IsHomalgSpectralSequence, IsList ] );
DeclareOperation( "StaircaseOfStability",
[ IsHomalgSpectralSequence, IsList, IsInt ] );
DeclareOperation( "StaircaseOfStability",
[ IsHomalgSpectralSequence, IsList ] );
[ Dauer der Verarbeitung: 0.25 Sekunden
(vorverarbeitet)
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