Currently a LazyFamily is automatically in EnumeratedSets, so at most countable.

We add keyword category to the constructor Family and all implementation classes, so that the user can choose the correct category.

Moreover, we define a (non-full) subcategory of Sets named Families, which captures the additional structure (= the map from the keys onto the parent).

Follow-ups / related:

• If the function from indices to objects is a morphism, then the category can be taken from the codomain.
• category of lazy family wrong if infinite combinatorial class used as index #18849 category of lazy family wrong if infinite combinatorial class used as index
• Bug in Family constructor #8822 Bug in Family constructor

Depends on #34375

CC: @tscrim

Component: combinatorics

Work Issues: Add method "as_map"

Author: Matthias Koeppe

Issue created by migration from https://trac.sagemath.org/ticket/34340