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11 The Category Constructor

11.1 Info class

11.1-1 InfoCategoryConstructor

Info class controlling the debugging output of CategoryConstructor (11.2-1).

11.2 Constructors

11.2-1 CategoryConstructor

Returns: a CAP category

Creates a CAP category subject to the options given via options, which is a record with the following keys:

• name (optional): name of the category

• category_filter, category_object_filter, category_morphism_filter (mandatory): passed to CreateCapCategoryWithDataTypes (1.3-4)

• object_datum_type, morphism_datum_type (optional): passed to CreateCapCategoryWithDataTypes (1.3-4)

• commutative_ring_of_linear_category (optional): ring attached as CommutativeRingOfLinearCategory (1.4-9) to the category

• range_category_of_homomorphism_structure (optional): category attached as RangeCategoryOfHomomorphismStructure (1.4-10) to the category (or the string "self" to attach the category to itself)

• properties (optional): list of categorical properties the category will have, see CAP_INTERNAL_CATEGORICAL_PROPERTIES_LIST

• object_constructor (optional): function added as an installation of ObjectConstructor (2.7-1) to the category

• object_datum (optional): function added as an installation of ObjectDatum (2.7-3) to the category

• morphism_constructor (optional): function added as an installation of MorphismConstructor (3.3-1) to the category

• morphism_datum (optional): function added as an installation of MorphismDatum (3.3-2) to the category

• list_of_operations_to_install (mandatory): a list of names of CAP operations which should be installed for the category

• is_computable (optional): whether the category can decide IsCongruentForMorphisms

• supports_empty_limits (optional): whether the category supports empty lists in inputs to operations of limits and colimits

• underlying_category_getter_string (optional): see below

• underlying_category (optional): see below

• underlying_object_getter_string (optional): see below

• underlying_morphism_getter_string (optional): see below

• top_object_getter_string (optional): see below

• top_morphism_getter_string (optional): see below

• generic_output_source_getter_string (optional): see below

• generic_output_range_getter_string (optional): see below

• create_func_bool: see below

• create_func_object: see below

• create_func_morphism: see below

• create_func_list_of_objects: see below

The values of the keys create_func_* should be either the string "default" or functions which accept the category and the name of a CAP operation of the corresponding return_type. Values for return types occuring for operations in list_of_operations_to_install are mandatory. The functions must return either strings or pairs of a string and an integer: The strings (after some replacements described below) will be evaluated and added as installations of the corresponding operations to the category with weights given by the integer (if provided). The value "default" chooses a suitable default string (see the implementation for details) and gets the weights from underlying_category. The following placeholders may be used in the strings and are replaced automatically:

• operation_name will be replaced by the name of the operation

• input_arguments... will be replaced by the input_arguments_names specified in the method name record (see 7.3)

• underlying_arguments...: If the constructed category is created from another category, underlying_category_getter_string, underlying_object_getter_string, and underlying_morphism_getter_string may be strings of functions computing the underlying category (when applied to the constructed category) and the underlying object resp. morphism (when applied to the constructed category and an object resp. morphism in the constructed category). These functions are applied to input_arguments and underlying_arguments is replaced by the result.

• number_of_arguments will be replaced by the number of input/underlying arguments

• top_source and top_range: If the return type is morphism, source and range are computed if possible and top_source and top_range are replaced by the results. For computing source and range, the output_source_getter_string and output_range_getter_string from the method name record are used if available (see 7.3). In some categories, source and range can always be obtained in a generic way (e.g. from the morphism datum). In this case, generic_output_source_getter_string and generic_output_range_getter_string can be set and are used if the required information is not available in the method name record.

• top_object_getter and top_morphism_getter are used in the "default" strings and are replaced by top_object_getter_string and top_morphism_getter_string, respectively.

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