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Quelle map2dnd.gd
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##############################################################################
##
#W map2dnd.gd GAP4 package `XMod' Chris Wensley
## Alper Odabas
#Y Copyright (C) 2001-2020, Chris Wensley et al,
##############################################################################
##
#C IsGeneral2DimensionalMapping( <map> )
#C IsNonSPGeneral2DimensionalMapping( <map> )
#C IsSPGeneral2DimensionalMapping( <map> )
##
#T do we need the SP and nonSP division ?
## Crossed module and cat1-group mapping declarations
DeclareCategory( "IsGeneral2DimensionalMapping", IsGeneralMapping );
DeclareCategory( "IsSPGeneral2DimensionalMapping",
IsSPGeneralMapping and IsGeneral2DimensionalMapping );
DeclareCategory( "IsNonSPGeneral2DimensionalMapping",
IsNonSPGeneralMapping and IsGeneral2DimensionalMapping );
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##
#C IsGeneral2DimensionalMappingCollection . . category of colls of mwo maps
#C IsGeneral2DimensionalMappingCollColl . . . category of colls of colls
#C IsGeneral2DimensionalMappingCollCollColl . category of colls, colls, colls
##
DeclareCategoryCollections( "IsGeneral2DimensionalMapping" );
DeclareCategoryCollections( "IsGeneral2DimensionalMappingCollection" );
DeclareCategoryCollections( "IsGeneral2DimensionalMappingCollColl" );
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##
#P Is2DimensionalMapping( <map> )
#P IsEndoGeneral2DimensionalMapping( <map> )
#P IsEndo2DimensionalMapping( <map> )
#P Is2DimensionalMagmaGeneralMapping( <map> )
#P Is2DimensionalMagmaMorphism( <map> )
#P Is2DimensionalSemigroupMorphism( <map> )
#P Is2DimensionalMonoidMorphism( <map> )
DeclareSynonymAttr( "Is2DimensionalMapping",
IsGeneral2DimensionalMapping and IsMapping );
DeclareSynonymAttr( "IsEndoGeneral2DimensionalMapping",
IsGeneral2DimensionalMapping and IsEndoGeneralMapping );
DeclareSynonymAttr( "IsEndo2DimensionalMapping",
Is2DimensionalMapping and IsEndoMapping );
DeclareSynonymAttr( "Is2DimensionalMagmaGeneralMapping",
IsGeneral2DimensionalMapping and RespectsMultiplication );
DeclareSynonymAttr( "Is2DimensionalMagmaMorphism",
Is2DimensionalMagmaGeneralMapping and IsMapping );
#? modify these next three to SynonymAttr's ??
DeclareProperty( "Is2DimensionalSemigroupMorphism",
Is2DimensionalMagmaMorphism );
DeclareProperty( "Is2DimensionalMonoidMorphism",
Is2DimensionalMagmaMorphism );
#############################################################################
##
#V General2DimensionalMappingFamily . family for homs of magmas with objects
#R Is2DimensionalMappingRep( <map> )
##
BindGlobal( "General2DimensionalMappingFamily",
NewFamily( "General2DimensionalMappingFamily", IsGeneral2DimensionalMapping,
CanEasilySortElements, CanEasilySortElements ) );
DeclareRepresentation( "Is2DimensionalMappingRep",
Is2DimensionalMagmaMorphism and IsAttributeStoringRep and IsGeneralMapping,
[ "Source", "Range", "SourceHom", "RangeHom" ] );
##############################################################################
##
#C Is2DimensionalGroupMorphism( <map> )
#C Is2DimensionalGroupMorphismCollection . category of colls of pre-xmod homs
#C Is2DimensionalGroupMorphismCollColl . . . . . . category of colls of colls
#C Is2DimensionalGroupMorphismCollCollColl . category of colls, colls, colls
#V Family2DimensionalGroupMorphism . . family for homomorphisms of pre-xmods
#T Type2DimensionalGroupMorphism . . . . type for homomorphisms of pre-xmods
##
DeclareCategory( "Is2DimensionalGroupMorphism", IsGeneral2DimensionalMapping );
DeclareCategoryCollections( "Is2DimensionalGroupMorphism" );
DeclareCategoryCollections( "Is2DimensionalGroupMorphismCollection" );
DeclareCategoryCollections( "Is2DimensionalGroupMorphismCollColl" );
BindGlobal( "Family2DimensionalGroupMorphism",
NewFamily( "Family2DimensionalGroupMorphism", Is2DimensionalGroupMorphism,
CanEasilySortElements, CanEasilySortElements ) );
BindGlobal( "Type2DimensionalGroupMorphism",
NewType( Family2DimensionalGroupMorphism,
Is2DimensionalMappingRep ) );
#############################################################################
##
#P IsPreXModMorphism( <map> )
#P IsPreCat1GroupMorphism( <map> )
#P IsXModMorphism( <map> )
#P IsCat1GroupMorphism( <map> )
##
DeclareProperty( "IsPreXModMorphism", Is2DimensionalGroupMorphism );
DeclareProperty( "IsPreCat1GroupMorphism", Is2DimensionalGroupMorphism );
DeclareProperty( "IsXModMorphism", IsPreXModMorphism );
DeclareProperty( "IsCat1GroupMorphism", IsPreCat1GroupMorphism );
##############################################################################
##
#A SourceHom( <mor> )
#A RangeHom( <mor> )
##
DeclareAttribute( "SourceHom", Is2DimensionalGroupMorphism );
DeclareAttribute( "RangeHom", Is2DimensionalGroupMorphism );
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##
## Make2DimensionalMagmaMorphism( <args> )
##
DeclareGlobalFunction( "Make2DimensionalMagmaMorphism" );
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##
#A Kernel2DimensionalMapping( <mor> )
##
DeclareAttribute( "Kernel2DimensionalMapping", Is2DimensionalGroupMorphism );
######################## HIGHER DIMENSIONAL MAPPINGS ######################
#############################################################################
##
#C IsGeneralHigherDimensionalMapping( <map> )
#C IsNonSPGeneralHigherDimensionalMapping( <map> )
#C IsSPGeneralHigherDimensionalMapping( <map> )
##
DeclareCategory( "IsGeneralHigherDimensionalMapping",
IsGeneral2DimensionalMapping );
DeclareCategory( "IsSPGeneralHigherDimensionalMapping",
IsGeneralHigherDimensionalMapping and IsSPGeneralMapping );
DeclareCategory( "IsNonSPGeneralHigherDimensionalMapping",
IsGeneralHigherDimensionalMapping and IsNonSPGeneralMapping );
#############################################################################
##
#C IsGeneralHigherDimensionalMapping
## . . . . . category of colls of higher dimensional magma maps
#C IsGeneralHigherDimensionalMappingCollColl . . category of colls of colls
##
DeclareCategoryCollections( "IsGeneralHigherDimensionalMapping" );
DeclareCategoryCollections( "IsGeneralHigherDimensionalMappingCollection" );
DeclareCategoryCollections( "IsGeneralHigherDimensionalMappingCollColl" );
#############################################################################
##
#P IsHigherDimensionalMapping( <map> )
#P IsEndoGeneralHigherDimensionalMapping( <map> )
#P IsEndoHigherDimensionalMapping( <map> )
#P IsHigherDimensionalMagmaGeneralMapping( <map> )
#P IsHigherDimensionalMagmaMorphism( <map> )
#P IsHigherDimensionalSemigroupMorphism( <map> )
#P IsHigherDimensionalMonoidMorphism( <map> )
DeclareSynonymAttr( "IsHigherDimensionalMapping",
IsGeneralHigherDimensionalMapping and IsMapping );
DeclareSynonymAttr( "IsEndoGeneralHigherDimensionalMapping",
IsGeneralHigherDimensionalMapping and IsEndoGeneralMapping );
DeclareSynonymAttr( "IsEndoHigherDimensionalMapping",
IsHigherDimensionalMapping and IsEndoMapping );
DeclareSynonymAttr( "IsHigherDimensionalMagmaGeneralMapping",
IsGeneralHigherDimensionalMapping and RespectsMultiplication );
DeclareSynonymAttr( "IsHigherDimensionalMagmaMorphism",
IsHigherDimensionalMagmaGeneralMapping and IsMapping );
DeclareProperty( "IsHigherDimensionalSemigroupMorphism",
IsHigherDimensionalMagmaMorphism );
DeclareProperty( "IsHigherDimensionalMonoidMorphism",
IsHigherDimensionalMagmaMorphism );
#############################################################################
##
#V GeneralHigherDimensionalMappingFamily
## . . . . family for homs of higher dimensional magmas with objects
#R IsHigherDimensionalMappingRep( <mor> )
##
BindGlobal( "GeneralHigherDimensionalMappingFamily",
NewFamily( "GeneralHigherDimensionalMappingFamily", IsGeneralHigherDimensionalMapping,
CanEasilySortElements, CanEasilySortElements ) );
DeclareRepresentation( "IsHigherDimensionalMappingRep",
IsHigherDimensionalMapping and IsAttributeStoringRep,
[ "Source", "Range", "ListOf2DimensionalMappings", "HigherDimension" ] );
##############################################################################
##
#C IsHigherDimensionalGroupMorphism( <map> )
#C IsHigherDimensionalGroupMorphismCollection
#C IsHigherDimensionalGroupMorphismCollColl .
#V FamilyHigherDimensionalGroupMorphism
#T Type2DimensionalGroupMorphism
##
DeclareCategory( "IsHigherDimensionalGroupMorphism",
IsGeneralHigherDimensionalMapping );
DeclareCategoryCollections( "IsHigherDimensionalGroupMorphism" );
DeclareCategoryCollections( "IsHigherDimensionalGroupMorphismCollection" );
DeclareCategoryCollections( "IsHigherDimensionalGroupMorphismCollColl" );
BindGlobal( "FamilyHigherDimensionalGroupMorphism",
NewFamily( "FamilyHigherDimensionalGroupMorphism",
IsHigherDimensionalGroupMorphism,
CanEasilySortElements, CanEasilySortElements ) );
BindGlobal( "TypeHigherDimensionalGroupMorphism",
NewType( FamilyHigherDimensionalGroupMorphism,
IsHigherDimensionalMappingRep ) );
#############################################################################
##
#C IsGeneral3DimensionalMapping( <map> )
#C IsNonSPGeneral3DimensionalMapping( <map> )
#C IsSPGeneral3DimensionalMapping( <map> )
##
DeclareCategory( "IsGeneral3DimensionalMapping", IsGeneral2DimensionalMapping );
DeclareCategory( "IsSPGeneral3DimensionalMapping",
IsGeneral3DimensionalMapping and IsSPGeneralMapping );
DeclareCategory( "IsNonSPGeneral3DimensionalMapping",
IsGeneral3DimensionalMapping and IsNonSPGeneralMapping );
#############################################################################
##
#P IsPreSqMorphism( <map> )
#P IsPreCat2GroupMorphism( <map> )
#P IsCrossedSquareMorphism( <map> )
#P IsCat2GroupMorphism( <map> )
##
DeclareProperty( "IsPreCrossedSquareMorphism",
IsHigherDimensionalGroupMorphism );
DeclareProperty( "IsPreCat2GroupMorphism", IsHigherDimensionalGroupMorphism );
DeclareProperty( "IsCrossedSquareMorphism", IsHigherDimensionalGroupMorphism );
DeclareProperty( "IsCat2GroupMorphism", IsHigherDimensionalGroupMorphism );
#############################################################################
##
#A Up2DimensionalMorphism( <mor> )
#A Left2DimensionalMorphism( <mor> )
#A Down2DimensionalMorphism( <mor> )
#A Right2DimensionalMorphism( <mor> )
##
## A pre-crossed square or pre-cat2-group morphism contains 4 group homs
##
DeclareAttribute( "Up2DimensionalMorphism", IsHigherDimensionalMapping );
DeclareAttribute( "Left2DimensionalMorphism", IsHigherDimensionalMapping );
DeclareAttribute( "Down2DimensionalMorphism", IsHigherDimensionalMapping );
DeclareAttribute( "Right2DimensionalMorphism", IsHigherDimensionalMapping );
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2026-03-28
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