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16 Terminal category
 16.1 GAP Categories
 16.2 Constructors
 16.3 Attributes

16 Terminal category

16.1 GAP Categories

16.1-1 IsCapTerminalCategoryWithSingleObject
‣ IsCapTerminalCategoryWithSingleObject( T )( filter )

Returns: true or false

The GAP type of a terminal category with a single object.

16.1-2 IsObjectInCapTerminalCategoryWithSingleObject
‣ IsObjectInCapTerminalCategoryWithSingleObject( T )( filter )

Returns: true or false

The GAP type of an object in a terminal category with a single object.

16.1-3 IsMorphismInCapTerminalCategoryWithSingleObject
‣ IsMorphismInCapTerminalCategoryWithSingleObject( T )( filter )

Returns: true or false

The GAP type of a morphism in a terminal category with a single object.

16.1-4 IsCapTerminalCategoryWithMultipleObjects
‣ IsCapTerminalCategoryWithMultipleObjects( T )( filter )

Returns: true or false

The GAP type of a terminal category with multiple objects.

16.1-5 IsObjectInCapTerminalCategoryWithMultipleObjects
‣ IsObjectInCapTerminalCategoryWithMultipleObjects( T )( filter )

Returns: true or false

The GAP type of an object in a terminal category with multiple objects.

16.1-6 IsMorphismInCapTerminalCategoryWithMultipleObjects
‣ IsMorphismInCapTerminalCategoryWithMultipleObjects( T )( filter )

Returns: true or false

The GAP type of a morphism in a terminal category with multiple objects.

16.1-7 IsTerminalCategory
‣ IsTerminalCategory( C )( property )

Returns: true or false

The property of the category C being terminal.

16.2 Constructors

16.2-1 TerminalCategoryWithSingleObject
‣ TerminalCategoryWithSingleObject( arg )( function )

Construct a terminal category with a single object.

16.2-2 TerminalCategoryWithMultipleObjects
‣ TerminalCategoryWithMultipleObjects( arg )( function )

Construct a terminal category with multiple objects.

16.2-3 CAP_INTERNAL_CONSTRUCTOR_FOR_TERMINAL_CATEGORY
‣ CAP_INTERNAL_CONSTRUCTOR_FOR_TERMINAL_CATEGORY( options )( function )

Returns: a CAP category

This function takes a record of options suited for CategoryConstructor. It makes common adjustments for TerminalCategoryWithSingleObject and TerminalCategoryWithMultipleObjects to the list of operations to install and the categorical properties of the given record, before passing it on to CategoryConstructor.

16.3 Attributes

16.3-1 UniqueObject
‣ UniqueObject( arg )( attribute )

Returns: a CAP object

The unique object in a terminal category with a single object.

16.3-2 UniqueMorphism
‣ UniqueMorphism( arg )( attribute )

Returns: a CAP morphism

The unique morphism in a terminal category with a single object.

16.3-3 FunctorFromTerminalCategory
‣ FunctorFromTerminalCategory( object )( attribute )

Returns: a CAP functor

A functor from AsCapCategory( TerminalObject( CapCat ) ) mapping the unique object to object.

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