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#W gpd2obj.gd GAP4 package `XMod' Chris Wensley
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#Y Copyright (C) 2001-2025, Chris Wensley et al,
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#C Is2DimensionalDomainWithObjects( <obj> )
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DeclareCategory( "Is2DimensionalDomainWithObjects",
Is2DimensionalDomain and IsDomainWithObjects );
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#C Is2DimensionalMagmaWithObjects( <m2d> ) category of 2d magmas with objects
#C Is2DimensionalMagmaWithObjectsAndOnes( <m2d> ) . . . . . . . and with ones
#C Is2DimensionalMagmaWithObjectsAndInverses( <m2d> ) . . . and some inverses
#C Is2DimensionalGroupWithObjects( <m2d> ) . . . . . . . . and all inverses
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DeclareCategory( "Is2DimensionalMagmaWithObjects",
Is2DimensionalDomainWithObjects and IsMagmaWithObjects );
DeclareCategoryCollections( "Is2DimensionalMagmaWithObjects" );
DeclareCategory( "Is2DimensionalMagmaWithObjectsAndOne",
Is2DimensionalMagmaWithObjects
and CategoryCollections( IsMultiplicativeElementWithObjectsAndOnes ) );
DeclareCategory( "Is2DimensionalMagmaWithObjectsAndInverses",
Is2DimensionalMagmaWithObjectsAndOne
and CategoryCollections( IsMultiplicativeElementWithObjectsAndInverses ) );
DeclareCategory( "Is2DimensionalGroupWithObjects",
Is2DimensionalMagmaWithObjectsAndInverses
and CategoryCollections( IsAssociativeElement ) );
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#V Family2DimensionalGroupWithObjects . . family for 2d-groups with objects
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BindGlobal( "Family2DimensionalGroupWithObjects",
NewFamily( "Family2DimensionalGroupWithObjects",
Is2DimensionalGroupWithObjects,
CanEasilySortElements, CanEasilySortElements ) );
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#P IsPreXModWithObjects( <PM> ) . . . . . . . . for a 2d-domain with objects
#P IsXModWithObjects( <PM> ) . . . . . . . . . for a 2d-domain with objects
#P IsPreCat1Groupoid( <PM> ) . . . . . . . . . for a 2d-domain with objects
#P IsCat1Groupoid( <PM> ) . . . . . . . . . . . for a 2d-domain with objects
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DeclareProperty( "IsPreXModWithObjects",
IsPreXMod and Is2DimensionalDomainWithObjects );
DeclareProperty( "IsXModWithObjects", IsPreXModWithObjects );
DeclareProperty( "IsPreCat1Groupoid", #? another condition??
Is2DimensionalDomainWithObjects );
DeclareProperty( "IsCat1Groupoid", IsPreCat1Groupoid );
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#R IsPreXModWithObjectsObj( <obj> ) . . . . for objects, boundary and action
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## A pre-crossed module of groupoids is a morphism preserving an action
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DeclareRepresentation( "IsPreXModWithObjectsObj",
Is2DimensionalDomainWithObjects and IsAttributeStoringRep,
[ "boundary", "action" ] );
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#T PreXModWithObjectsType . . . . . . . . . . type for prexmods with objects
#T PreXModWithPiecesType . . . . . type for unions of prexmods with objects
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BindGlobal( "PreXModWithObjectsType",
NewType( Family2DimensionalGroupWithObjects,
IsPreXModWithObjectsObj ) );
BindGlobal( "PreXModWithPiecesType",
NewType( Family2DimensionalGroupWithObjects,
IsPreXModWithObjectsObj and IsPiecesRep ) );
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#O PreXModWithObjectsByBoundaryAndAction( <bdy>, <act> )
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DeclareOperation( "PreXModWithObjectsByBoundaryAndAction",
[ IsGroupoidHomomorphism, IsGroupoidHomomorphism ] );
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#A Root2dGroup( <dwo> )
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DeclareAttribute( "Root2dGroup", Is2DimensionalDomainWithObjects );
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#F PreXModWithObjects( <args> )
#O PreXModWithObjectsObj( <bdy>, <act> )
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DeclareGlobalFunction( "PreXModWithObjects" );
DeclareOperation( "PreXModWithObjectsObj",
[ IsGroupoidHomomorphism, IsGroupoidHomomorphism ] );
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#O SinglePiecePreXModWithObjects( <xmod>, <obs>, <isdiscrete> )
#O SinglePiecePreXModWithObjectsNC( <xmod>, <obs>, <isdiscrete>
## . . for precrossed modules, a set of objects, discrete or connected source
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DeclareOperation( "SinglePiecePreXModWithObjects",
[ IsPreXMod, IsList, IsBool ] );
DeclareOperation( "SinglePiecePreXModWithObjectsNC",
[ IsPreXMod, IsList, IsBool ] );
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#P IsPermPreXModWithObjects
#P IsPcPreXModWithObjects
#P IsFpPreXModWithObjects
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DeclareProperty( "IsPermPreXModWithObjects", Is2DimensionalDomainWithObjects );
DeclareProperty( "IsPcPreXModWithObjects", Is2DimensionalDomainWithObjects );
DeclareProperty( "IsFpPreXModWithObjects", Is2DimensionalDomainWithObjects );
