Quelle FiniteSkeletalDiscreteCategory.gi Sprache: unbekannt

# SPDX-License-Identifier: GPL-2.0-or-later
# CAP: Categories, Algorithms, Programming
#
# Implementations
#

InstallTrueMethod( IsDiscreteCategory, IsTerminalCategory );

####################################
#
# Constructor
#
####################################

##
InstallGlobalFunction( FiniteSkeletalDiscreteCategory,

  FunctionWithNamedArguments(
  [
    [ "FinalizeCategory", true ],
  ],
  function( CAP_NAMED_ARGUMENTS, list_of_gap_objects )
    local name, D;

    name := Concatenation( "FiniteSkeletalDiscreteCategory( ", String( list_of_gap_objects ), " )" );

    D := CreateCapCategoryWithDataTypes( name,
                                         IsFiniteSkeletalDiscreteCategory,
                                         IsObjectInFiniteSkeletalDiscreteCategory,
                                         IsMorphismInFiniteSkeletalDiscreteCategory,
                                         IsCapCategoryTwoCell,
                                         rec( category := false,
                                              filter := IsObject ),
                                         fail,
                                         fail );

    D!.compiler_hints := rec( category_attribute_names := [ "UnderlyingListOfGapObjects" ] );

    SetUnderlyingListOfGapObjects( D, list_of_gap_objects );

    SetIsFiniteCategory( D, true );

    SetIsSkeletalCategory( D, true );

    SetIsDiscreteCategory( D, true );

    ####################################
    #
    # Primitive operations
    #
    ####################################

    ##
    AddObjectConstructor( D,
      function( D, gap_object )

        #% CAP_JIT_DROP_NEXT_STATEMENT
        Assert( 0, gap_object in UnderlyingListOfGapObjects( D ) );

        return CreateCapCategoryObjectWithAttributes( D,
                                                      UnderlyingGapObject, gap_object );

    end );

    ##
    AddObjectDatum( D,
      function( D, object )

        return UnderlyingGapObject( object );

    end );

    ##
    AddMorphismConstructor( D,
      function( D, source, m, target )

        #% CAP_JIT_DROP_NEXT_STATEMENT
        Assert( 0, IsEqualForObjects( D, source, target ) );

        return CreateCapCategoryMorphismWithAttributes( D, source, target );

    end );

    ##
    AddMorphismDatum( D,
      function( D, morphism )

        return fail;

    end );

    ##
    AddIsWellDefinedForObjects( D,
      function( D, object )

        return UnderlyingGapObject( object ) in UnderlyingListOfGapObjects( D );

    end );

    ##
    AddIsWellDefinedForMorphisms( D,
      function( D, morphism )

        return IsEndomorphism( D, morphism ) and IsOne( D, morphism );

    end );

    AddIsEqualForObjects( D,
      function( D, object_1, object_2 )

        return UnderlyingGapObject( object_1 ) = UnderlyingGapObject( object_2 );

    end );

    ##
    AddIsEqualForMorphisms( D,
      function( D, morphism_1, morphism_2 )

        return true;

    end );

    ##
    AddIdentityMorphism( D,
      function( D, object )

        return MorphismConstructor( D, object, fail, object );

    end );

    ##
    AddPreCompose( D,
      function( D, morphism_1, morphism_2 )

        return morphism_1;

    end );

    ##
    AddSetOfObjectsOfCategory( D,
      function( D )

        return List( UnderlyingListOfGapObjects( D ), obj -> ObjectConstructor( D, obj ) );

    end );

    ##
    AddSetOfMorphismsOfFiniteCategory( D,
      function( D )

        return List( SetOfObjectsOfCategory( D ), obj -> IdentityMorphism( D, obj ) );

    end );

    if CAP_NAMED_ARGUMENTS.FinalizeCategory then

        Finalize( D );

    fi;

    return D;

end ) );

#################################
#
# Operators
#
#################################

##
InstallOtherMethod( \[\],
               "for a finite skeletal discrete category and a positive integer",
               [ IsFiniteSkeletalDiscreteCategory, IsInt ],

  function ( D, index )
    local objects;

    objects := SetOfObjectsOfCategory( D );

    if index <= 0 or index > Length( objects ) then

        # COVERAGE_IGNORE_NEXT_LINE
        Error( "out of bounds access\n" );

    fi;

    return objects[index];

end );

#################################
#
# View & Display
#
#################################

##
InstallMethod( DisplayString,
        [ IsObjectInFiniteSkeletalDiscreteCategory ],

  function( object )

    return Concatenation( String( UnderlyingGapObject( object ) ), "\n" );

end );

##
InstallMethod( DisplayString,
        [ IsMorphismInFiniteSkeletalDiscreteCategory ],

  function( morphism )

    return Concatenation( DisplayString( Source( morphism ) ),
                          "|\n| ",
                          String( morphism ),
                          "\nv\n",
                          DisplayString( Target( morphism ) ) );

end );

Quelle FiniteSkeletalDiscreteCategory.gi Sprache: unbekannt

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