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12 Create wrapper hulls of a category
 12.1 GAP categories
 12.2 Attributes
 12.3 Constructors

12 Create wrapper hulls of a category

The support for building towers of category constructors is one of the main design features of CAP. Many categories that appear in the various applications can be modeled by towers of multiple category constructors. The wrapper category constructor allows adding one last layer on top which allows expressing the desired (re)interpretation of such a modeling tower. In particular, the wrapper category constructor allows specifying the name of the category together with customized methods for the operations

in order to reflect the desired interpretation with a user-interface that is independent of the modeling tower. Note that the same tower might have multiple interpretations.

Table: A tower of categories modeling the category W
W := WrapperCategory( cat_n )
cat_n := CategoryConstructor_n( cat_{n-1} )
...
cat_1 := CategoryConstructor_1( non_categorical_input )

The wrapper category W is by construction equivalent to the top category cat_n in the tower. In practice, the word "tower" stands more generally for a finite poset with a greatest element.

12.1 GAP categories

12.1-1 IsWrapperCapCategory
‣ IsWrapperCapCategory( arg )( filter )

Returns: true or false

The GAP category of a wrapper CAP category (using the default data structure).

12.1-2 IsWrapperCapCategoryObject
‣ IsWrapperCapCategoryObject( arg )( filter )

Returns: true or false

The GAP category of objects in a wrapper CAP category.

12.1-3 IsWrapperCapCategoryMorphism
‣ IsWrapperCapCategoryMorphism( arg )( filter )

Returns: true or false

The GAP category of morphisms in a wrapper CAP category.

12.2 Attributes

12.2-1 ModelingCategory
‣ ModelingCategory( category )( attribute )

Returns: a category

The category used to model the wrapper category category.

12.2-2 UnderlyingCell
‣ UnderlyingCell( object )( attribute )

Returns: a category object

The cell underlying the wrapper category object object.

12.2-3 UnderlyingCell
‣ UnderlyingCell( morphism )( attribute )

Returns: a category morphism

The cell underlying the wrapper category morphism morphism.

12.3 Constructors

12.3-1 AsObjectInWrapperCategory
‣ AsObjectInWrapperCategory( category, object )( operation )

Returns: an object

Wrap an object object (in the category underlying the wrapper category category) to form an object in category.

12.3-2 AsMorphismInWrapperCategory
‣ AsMorphismInWrapperCategory( source, morphism, range )( operation )

Returns: a morphism

Wrap a morphism morphism (in the category underlying the wrapper category CapCategory(source)) to form a morphism in CapCategory(source) with given source and range.

12.3-3 AsMorphismInWrapperCategory
‣ AsMorphismInWrapperCategory( category, morphism )( operation )

Returns: a morphism

Wrap a morphism morphism (in the category underlying the wrapper category category) to form a morphism in category.

12.3-4 /
‣ /( cell, category )( operation )

Convenience method for AsObjectInWrapperCategory (12.3-1) and AsMorphismInWrapperCategory (12.3-3).

12.3-5 WrapperCategory
‣ WrapperCategory( category, options )( operation )

Returns: a category

Wraps a category category to form a new category subject to the options given via options, which is a record with the following keys:

Additionally, the following options of CategoryConstructor (11.2-1) are supported: category_filter, category_object_filter, category_morphism_filter, object_constructor, object_datum, morphism_constructor, morphism_datum. To avoid inconsistencies, either all or none of those options should be set. If they are set, also the following options should be set:

12.3-6 WrappingFunctor
‣ WrappingFunctor( W )( attribute )

Returns: a functor

Return the functor from the wrapped category ModelingCategory(W) to the wrapper category W. The functor maps each wrapped object/morphism to its wrapping object/morphism.

12.3-7 ModelingObject
‣ ModelingObject( cat, obj )( operation )

Returns: a CAP category object

Returns the object modeling the object obj in cat. cat must be a CAP category which has been created as a wrapper CAP category (but not necessarily uses the default data structure).

12.3-8 ModeledObject
‣ ModeledObject( cat, obj )( operation )

Returns: a CAP category object

Returns the object modeled by the object obj in the modeling category of cat. cat must be a CAP category which has been created as a wrapper CAP category (but not necessarily uses the default data structure).

12.3-9 ModelingMorphism
‣ ModelingMorphism( cat, mor )( operation )

Returns: a CAP category morphism

Returns the morphism modeling the morphism mor in cat. cat must be a CAP category which has been created as a wrapper CAP category (but not necessarily uses the default data structure).

12.3-10 ModeledMorphism
‣ ModeledMorphism( cat, source, obj, range )( operation )

Returns: a CAP category morphism

Returns the morphism modeled by the morphism mor in the modeling category of cat with given source and range. cat must be a CAP category which has been created as a wrapper CAP category (but not necessarily uses the default data structure).

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