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##############################################################################
##
#W gp3map.gd GAP4 package `XMod' Chris Wensley
## Alper Odabas
## This file declares functions for 3dimensional-mappings:
## (pre-)crossed squares and (pre-)cat2-groups.
##
#Y Copyright (C) 2001-2020, Chris Wensley et al,
#############################################################################
##
#O PreCrossedSquareMorphismByPreXModMorphisms( <src>, <rng>, <list> )
#O PreCrossedSquareMorphismByGroupHomomorphisms( <src>, <rng>, <list> )
#F PreCat2GroupMorphism( <args> )
#O PreCat2GroupMorphismByPreCat1GroupMorphisms( <src>, <rng>, <upm>, <ltm> )
#O PreCat2GroupMorphismByGroupHomomorphisms( <src>, <rng>, <list> )
##
DeclareGlobalFunction( "PreCrossedSquareMorphism" );
DeclareOperation( "PreCrossedSquareMorphismByPreXModMorphisms",
[ IsPreCrossedSquare, IsPreCrossedSquare, IsList ] );
DeclareOperation( "PreCrossedSquareMorphismByGroupHomomorphisms",
[ IsPreCrossedSquare, IsPreCrossedSquare, IsList ] );
DeclareGlobalFunction( "PreCat2GroupMorphism" );
DeclareOperation( "PreCat2GroupMorphismByPreCat1GroupMorphisms",
[ IsPreCat2Group, IsPreCat2Group, IsPreCat1GroupMorphism,
IsPreCat1GroupMorphism ] );
DeclareOperation( "PreCat2GroupMorphismByGroupHomomorphisms",
[ IsPreCat2Group, IsPreCat2Group, IsList ] );
#############################################################################
##
#F CrossedSquareMorphism( <args> )
#O CrossedSquareMorphismByXModMorphisms( <src>, <rng>, <list> )
#O CrossedSquareMorphismByGroupHomomorphisms( <src>, <rng>, <list> )
#F Cat2GroupMorphism( <args> )
#O Cat2GroupMorphismByCat1GroupMorphisms( <src>, <rng>, <upm>, <ltm> )
#O Cat2GroupMorphismByGroupHomomorphisms( <src>, <rng>, <homs> )
#O InclusionMorphismHigherDimensionalDomains( <obj>, <sub> )
##
DeclareGlobalFunction( "CrossedSquareMorphism" );
DeclareOperation( "CrossedSquareMorphismByXModMorphisms",
[ IsCrossedSquare, IsCrossedSquare, IsList ] );
DeclareOperation( "CrossedSquareMorphismByGroupHomomorphisms",
[ IsCrossedSquare, IsCrossedSquare, IsList ] );
DeclareGlobalFunction( "Cat2GroupMorphism" );
DeclareOperation( "Cat2GroupMorphismByCat1GroupMorphisms",
[ IsCat2Group, IsCat2Group, IsCat1GroupMorphism, IsCat1GroupMorphism ] );
DeclareOperation( "Cat2GroupMorphismByGroupHomomorphisms",
[ IsCat2Group, IsCat2Group, IsList ] );
DeclareOperation( "InclusionMorphismHigherDimensionalDomains",
[ IsHigherDimensionalDomain, IsHigherDimensionalDomain ] );
#############################################################################
##
#O InnerAutomorphismCrossedSquare( <XM>, <r> )
#O InnerAutomorphismCat2Group( <C1G>, <r> )
##
DeclareOperation( "InnerAutomorphismCrossedSquare",
[ IsPreCrossedSquare, IsMultiplicativeElementWithInverse ] );
DeclareOperation( "InnerAutomorphismCat2Group",
[ IsPreCat2Group, IsMultiplicativeElementWithInverse ] );
#############################################################################
##
#A CrossedSquareMorphismOfCat2GroupMorphism( <mor> )
#A Cat2GroupMorphismOfCrossedSquareMorphism( <mor> )
##
DeclareAttribute( "CrossedSquareMorphismOfCat2GroupMorphism",
IsCat2GroupMorphism );
DeclareAttribute( "Cat2GroupMorphismOfCrossedSquareMorphism",
IsCrossedSquareMorphism );
#############################################################################
##
#O Display3DimensionalMorphism( <mor )
##
DeclareOperation( "Display3DimensionalMorphism",
[ IsHigherDimensionalMapping ] );
#############################################################################
##
#O IsomorphismPreCat2GroupsNoTranspose( <precat2>, <precat2> )
#O IsomorphismCat2GroupsNoTranspose( <cat2>, <cat2> ) ?? is this needed ??
#O IsomorphismPreCat2Groups( <precat2>, <precat2> )
#O IsomorphismCat2Groups( <cat2>, <cat2> )
##
DeclareOperation( "IsomorphismPreCat2GroupsNoTranspose",
[ IsPreCat2Group, IsPreCat2Group ] );
DeclareOperation( "IsomorphismCat2GroupsNoTranspose",
[ IsCat2Group, IsCat2Group ] );
DeclareOperation( "IsomorphismPreCat2Groups",
[ IsPreCat2Group, IsPreCat2Group ] );
DeclareOperation( "IsomorphismCat2Groups",
[ IsCat2Group, IsCat2Group ] );
#############################################################################
##
#O AllCat2GroupMorphisms( <cat2>, <cat2> )
##
DeclareOperation( "AllCat2GroupMorphisms", [ IsCat2Group, IsCat2Group ] );
[ Dauer der Verarbeitung: 0.18 Sekunden
(vorverarbeitet)
]
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