3.1 Creating Categories

NewCategory returns a new category cat that has the name name and is contained in the filter super, see Filters in the Reference Manual. This means that every object in cat lies automatically also in super. We say also that super is an implied filter of cat.

For example, if one wants to create a category of group elements then super should be IsMultiplicativeElementWithInverse or a subcategory of it. If no specific supercategory of cat is known, super may be IsObject.

@Eventually tools will be provided to display hierarchies of categories etc., which will help to choose super appropriately.@

The incremental rank (see Filters in the Reference Manual) of cat is 1.

Two functions that return special kinds of categories are of importance.

For a category cat, CategoryCollections returns the collections category of cat. This is a category in that all collections of objects in cat lie.

For example, a permutation lies in the category IsPerm, and every dense list of permutations and every domain of permutations lies in the collections category of IsPerm.

For a category cat, CategoryFamily returns the family category of cat. This is a category in that all families lie that know from their creation that all their elements are in the category cat, see Creating Families.

For example, a family of tuples is in the category CategoryFamily( IsTuple ), and one can distinguish such a family from others by this category. So it is possible to install methods for operations that require one argument to be a family of tuples.

CategoryFamily is quite technical, and in fact of minor importance.

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