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15 Terminal category
 15.1 GAP Categories
 15.2 Constructors
 15.3 Attributes

15 Terminal category

15.1 GAP Categories

15.1-1 IsCapTerminalCategoryWithSingleObject
‣ IsCapTerminalCategoryWithSingleObject( T )( filter )

Returns: true or false

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

15.1-2 IsObjectInCapTerminalCategoryWithSingleObject
‣ IsObjectInCapTerminalCategoryWithSingleObject( T )( filter )

Returns: true or false

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

15.1-3 IsMorphismInCapTerminalCategoryWithSingleObject
‣ IsMorphismInCapTerminalCategoryWithSingleObject( T )( filter )

Returns: true or false

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

15.1-4 IsCapTerminalCategoryWithMultipleObjects
‣ IsCapTerminalCategoryWithMultipleObjects( T )( filter )

Returns: true or false

The GAP type of a terminal category with multiple objects.

15.1-5 IsObjectInCapTerminalCategoryWithMultipleObjects
‣ IsObjectInCapTerminalCategoryWithMultipleObjects( T )( filter )

Returns: true or false

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

15.1-6 IsMorphismInCapTerminalCategoryWithMultipleObjects
‣ IsMorphismInCapTerminalCategoryWithMultipleObjects( T )( filter )

Returns: true or false

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

15.1-7 IsTerminalCategory
‣ IsTerminalCategory( C )( property )

Returns: true or false

The property of the category C being terminal.

15.2 Constructors

15.2-1 TerminalCategoryWithSingleObject
‣ TerminalCategoryWithSingleObject( arg )( function )

Construct a terminal category with a single object.

15.2-2 TerminalCategoryWithMultipleObjects
‣ TerminalCategoryWithMultipleObjects( arg )( function )

Construct a terminal category with multiple objects.

15.2-3 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.

15.3 Attributes

15.3-1 UniqueObject
‣ UniqueObject( arg )( attribute )

Returns: a CAP object

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

15.3-2 UniqueMorphism
‣ UniqueMorphism( arg )( attribute )

Returns: a CAP morphism

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

15.3-3 FunctorFromTerminalCategory
‣ FunctorFromTerminalCategory( object )( attribute )

Returns: a CAP functor

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

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