|
# SPDX-License-Identifier: GPL-2.0-or-later
# homalg: A homological algebra meta-package for computable Abelian categories
#
# Declarations
#
## Declaration stuff for a filtration.
####################################
#
# categories:
#
####################################
# A new GAP-category:
## <#GAPDoc Label="IsHomalgFiltration">
## <ManSection>
## <Filt Type="Category" Arg="filt" Name="IsHomalgFiltration"/>
## <Returns><C>true</C> or <C>false</C></Returns>
## <Description>
## The &GAP; category of &homalg; filtrations.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareCategory( "IsHomalgFiltration",
IsAttributeStoringRep );
## CAUTION: in the code the following two categories are the only ones for sets of generators,
## i.e. IsHomalgFiltration and not IsHomalgFiltrationOfLeftObject => IsHomalgFiltrationOfRightObject
DeclareCategory( "IsHomalgFiltrationOfLeftObject",
IsHomalgFiltration );
DeclareCategory( "IsHomalgFiltrationOfRightObject",
IsHomalgFiltration );
DeclareCategory( "IsDescendingFiltration",
IsHomalgFiltration );
DeclareCategory( "IsAscendingFiltration",
IsHomalgFiltration );
####################################
#
# properties:
#
####################################
DeclareProperty( "IsGradation",
IsHomalgFiltration );
DeclareProperty( "IsFiltration",
IsHomalgFiltration );
DeclareProperty( "IsPurityFiltration",
IsHomalgFiltration );
DeclareProperty( "IsCompletePurityFiltration",
IsHomalgFiltration );
####################################
#
# attributes:
#
####################################
## <#GAPDoc Label="SpectralSequence:filt">
## <ManSection>
## <Attr Arg="BC" Name="SpectralSequence" Label="for filtrations"/>
## <Returns>a &homalg; (co)homological spectral sequence</Returns>
## <Description>
## The spectral sequence used to construct the filtration (if any).
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "SpectralSequence",
IsHomalgFiltration );
####################################
#
# global functions and operations:
#
####################################
# constructors:
DeclareGlobalFunction( "HomalgFiltration" );
DeclareGlobalFunction( "HomalgFiltrationFromTelescope" );
DeclareGlobalFunction( "HomalgFiltrationFromTower" );
DeclareGlobalFunction( "HomalgDescendingFiltration" );
DeclareGlobalFunction( "HomalgAscendingFiltration" );
# basic operations:
DeclareOperation( "DegreesOfFiltration",
[ IsHomalgFiltration ] );
DeclareOperation( "LowestDegree",
[ IsHomalgFiltration ] );
DeclareOperation( "HighestDegree",
[ IsHomalgFiltration ] );
DeclareOperation( "CertainMorphism",
[ IsHomalgFiltration, IsInt ] );
DeclareOperation( "CertainObject",
[ IsHomalgFiltration, IsInt ] );
DeclareOperation( "ObjectsOfFiltration",
[ IsHomalgFiltration ] );
DeclareOperation( "LowestDegreeObject",
[ IsHomalgFiltration ] );
DeclareOperation( "HighestDegreeObject",
[ IsHomalgFiltration ] );
DeclareOperation( "StructureObject",
[ IsHomalgFiltration ] );
DeclareOperation( "MorphismsOfFiltration",
[ IsHomalgFiltration ] );
DeclareOperation( "LowestDegreeMorphism",
[ IsHomalgFiltration ] );
DeclareOperation( "HighestDegreeMorphism",
[ IsHomalgFiltration ] );
if IsBoundGlobal( "UnderlyingObject" ) and not IsAttribute( ValueGlobal( "UnderlyingObject" ) ) then
DeclareOperation( "UnderlyingObject", [ IsHomalgFiltration ] );
else
DeclareAttribute( "UnderlyingObject", IsHomalgFiltration );
fi;
DeclareOperation( "IsomorphismOfFiltration",
[ IsHomalgFiltration ] );
DeclareOperation( "UnlockObject",
[ IsHomalgFiltration ] );
DeclareOperation( "AssociatedSecondSpectralSequence",
[ IsHomalgFiltration ] );
DeclareOperation( "*",
[ IsHomalgFiltration, IsHomalgStaticMorphism ] );
[ Dauer der Verarbeitung: 0.16 Sekunden
(vorverarbeitet)
]
|
