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##
#W gpdhom.gd GAP4 package `groupoids' Chris Wensley
#W & Emma Moore
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##
## GroupoidHomomorphism( <args> )
##
DeclareGlobalFunction( "GroupoidHomomorphism" );
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#A IsomorphismPermGroupoid( <gpd> )
#A IsomorphismPcGroupoid( <gpd> )
#A RegularActionHomomorphismGroupoid( <gpd> )
##
DeclareAttribute( "IsomorphismPermGroupoid", IsGroupoid );
DeclareAttribute( "IsomorphismPcGroupoid", IsGroupoid );
DeclareAttribute( "RegularActionHomomorphismGroupoid", IsGroupoid );
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#P IsGroupoidEndomorphism( <mor> )
DeclareSynonym( "IsGroupoidEndomorphism",
IsGroupoidHomomorphism and IsEndomorphismWithObjects );
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#O InclusionMappingGroupoids( <G>, <H> )
#O RestrictedMappingGroupoids( <hom>, <src> )
#A ParentMappingGroupoids( <hom> )
##
DeclareOperation( "InclusionMappingGroupoids", [ IsGroupoid, IsGroupoid ] );
DeclareOperation( "RestrictedMappingGroupoids",
[ IsGeneralMappingWithObjects, IsGroupoid ] );
DeclareAttribute( "ParentMappingGroupoids", IsGeneralMappingWithObjects );
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#O IsomorphismStandardGroupoid( <gpd>, <obs> )
##
DeclareOperation( "IsomorphismStandardGroupoid",
[ IsGroupoid, IsHomogeneousList ] );
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#O IsomorphismGroupoids( <gpd1>, <gpd2> )
##
DeclareOperation( "IsomorphismGroupoids", [ IsGroupoid, IsGroupoid ] );
####################### functions from the 08.05 paper #######################
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#R IsDefaultGroupoidHomomorphismRep( <map> )
##
## A mapping of connected groupoids is determined by:
## - mapping from the root group in the source to that in the range,
## - images for the objects,
## - images for the rays.
## In this representation, however, we just store the source; the range; and
## then put all the necessary detail into the list MappingToSinglePieceData.
## This third attribute can vary in contents, according to context.
## For general groupoids a PieceImage is a list [hom,oims,rims],
## giving a root group hom; list of object images; list of ray images.
##
DeclareRepresentation( "IsDefaultGroupoidHomomorphismRep",
IsGroupoidHomomorphism and IsAttributeStoringRep and IsComponentObjectRep,
[ "Source", "Range", "PiecesOfMapping" ] );
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#V GroupoidHomomorphismFamily . . . . family for homomorphisms of groupoids
#T GroupoidHomomorphismType . . . . . . type for homomorphisms of groupoids
##
BindGlobal( "GroupoidHomomorphismFamily",
NewFamily( "GroupoidHomomorphismFamily", IsGroupoidHomomorphism,
CanEasilySortElements, CanEasilySortElements ) );
BindGlobal( "GroupoidHomomorphismType",
NewType( GroupoidHomomorphismFamily,
IsDefaultGroupoidHomomorphismRep and IsGroupoidHomomorphism ) );
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#O MappingPermObjectsImages( <obs>, <ims> )
#O MappingTransObjectsImages( <obs>, <ims> )
#A ObjectTransformationOfGroupoidHomomorphism( <hom> )
##
DeclareOperation( "MappingPermObjectsImages", [ IsList, IsList ] );
DeclareOperation( "MappingTransObjectsImages", [ IsList, IsList ] );
DeclareAttribute( "ObjectTransformationOfGroupoidHomomorphism",
IsGroupWithObjectsHomomorphism );
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#A RootGroupHomomorphism( <map> )
#O ObjectGroupHomomorphism( <map>, <obj> )
#O GroupoidHomomorphismFromSinglePieceNC( <src>, <rng>, <gens>, <images> )
#O GroupoidHomomorphismFromSinglePiece( <src>, <rng>, <gens>, <images> )
##
DeclareAttribute( "RootGroupHomomorphism",
IsGroupoidHomomorphism and IsHomomorphismToSinglePiece );
DeclareOperation( "ObjectGroupHomomorphism",
[ IsGroupoidHomomorphism, IsObject ] );
DeclareOperation( "GroupoidHomomorphismFromSinglePieceNC",
[ IsGroupoid, IsGroupoid, IsHomogeneousList, IsHomogeneousList ] );
DeclareOperation( "GroupoidHomomorphismFromSinglePiece",
[ IsGroupoid, IsGroupoid, IsHomogeneousList, IsHomogeneousList ] );
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#O TestAllProductsUnderGroupoidHomomorphism( <hom> )
##
DeclareOperation( "TestAllProductsUnderGroupoidHomomorphism",
[ IsGroupoidHomomorphism ] );
## ======================================================================== ##
## Homogeneous groupoid homomorphisms ##
## ======================================================================== ##
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#R IsGroupoidHomomorphismFromHomogeneousDiscreteRep( <map> )
##
## A groupoid mapping from a homogeneous, discrete groupoid is determined by:
## - homs from the object groups in the source to those in the range,
## - images for the objects.
##
DeclareRepresentation( "IsGroupoidHomomorphismFromHomogeneousDiscreteRep",
IsGroupoidHomomorphism and IsAttributeStoringRep and IsComponentObjectRep,
[ "Source", "Range", "ImagesOfObjects", "ObjectHomomorphisms" ] );
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#O GroupoidHomomorphismFromHomogeneousDiscrete( <src>,<rng>,<homs>,<oims> )
#O GroupoidHomomorphismFromHomogeneousDiscreteNC( <src>,<rng>,<homs>,<oims> )
#A ObjectHomomorphisms( <map> )
#P IsGeneralMappingFromHomogeneousDiscrete( <map> )
#P IsGroupoidHomomorphismFromHomogeneousDiscrete( <map> )
#P IsGroupoidHomomorphismWithGroupoidByIsomorphisms( <map> )
##
DeclareOperation( "GroupoidHomomorphismFromHomogeneousDiscrete",
[ IsHomogeneousDiscreteGroupoid, IsGroupoid, IsHomogeneousList,
IsHomogeneousList ] );
DeclareOperation( "GroupoidHomomorphismFromHomogeneousDiscreteNC",
[ IsHomogeneousDiscreteGroupoid, IsGroupoid, IsHomogeneousList,
IsHomogeneousList ] );
DeclareAttribute( "ObjectHomomorphisms",
IsGroupoidHomomorphism and IsHomomorphismToSinglePiece );
DeclareProperty( "IsGeneralMappingFromHomogeneousDiscrete",
IsGeneralMappingWithObjects );
DeclareProperty( "IsGroupoidHomomorphismFromHomogeneousDiscrete",
IsGeneralMappingWithObjects );
DeclareProperty( "IsGroupoidHomomorphismWithGroupoidByIsomorphisms",
IsGeneralMappingWithObjects );
