GAP (CAP) - Chapter 13: Create wrapper hulls of a category

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13 Create wrapper hulls of a category
13.1 GAP categories
13.1-1 IsWrapperCapCategory
13.1-2 IsWrapperCapCategoryObject
13.1-3 IsWrapperCapCategoryMorphism
13.2 Attributes
13.2-1 UnderlyingCell
13.2-2 UnderlyingCell
13.3 Constructors
13.3-1 AsObjectInWrapperCategory
13.3-2 AsMorphismInWrapperCategory
13.3-3 AsMorphismInWrapperCategory
13.3-4 /
13.3-5 WrapperCategory
13.3-6 WrappingFunctor

### 13 Create wrapper hulls of a category

#### 13.1 GAP categories

##### 13.1-1 IsWrapperCapCategory

`‣ IsWrapperCapCategory`( arg ) | ( filter )

Returns: `true` or `false`

The GAP category of a wrapper CAP category.

##### 13.1-2 IsWrapperCapCategoryObject

`‣ IsWrapperCapCategoryObject`( arg ) | ( filter )

Returns: `true` or `false`

The GAP category of objects in a wrapper CAP category.

##### 13.1-3 IsWrapperCapCategoryMorphism

`‣ IsWrapperCapCategoryMorphism`( arg ) | ( filter )

Returns: `true` or `false`

The GAP category of morphisms in a wrapper CAP category.

#### 13.2 Attributes

##### 13.2-1 UnderlyingCell

`‣ UnderlyingCell`( object ) | ( attribute )

Returns: a category object

The cell underlying the wrapper category object object.

##### 13.2-2 UnderlyingCell

`‣ UnderlyingCell`( morphism ) | ( attribute )

Returns: a category morphism

The cell underlying the wrapper category morphism morphism.

#### 13.3 Constructors

##### 13.3-1 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.

##### 13.3-2 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.

##### 13.3-3 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.

##### 13.3-4 /

`‣ /`( cell, category ) | ( operation )

Convenience method for `AsObjectInWrapperCategory` (13.3-1) and `AsMorphismInWrapperCategory` (13.3-3).

##### 13.3-5 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:

- `name` (optional): the name of the wrapper category

- `only_primitive_operations` (optional, default `false`): whether to only wrap primitive operations or all operations

Additionally, the following options of `CategoryConstructor` (11.2-1) are supported: `category_filter`, `category_object_filter`, `category_morphism_filter`. The filters must imply `IsWrapperCapCategory`, `IsWrapperCapCategoryObject`, and `IsWrapperCapCategoryMorphism`, respectively.

##### 13.3-6 WrappingFunctor

`‣ WrappingFunctor`( W ) | ( attribute )

Returns: a functor

Return the functor from the wrapped category `ModelingCategory`(W) to the wrapper category W which simply wraps objects/morphisms.

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