Implement an_instance for more categories, and extend category_sample

[nthiery]

category_sample should look deeper in the code to find categories. It
currently only looks into sage.categories.all, and misses axiom or
covariant functorial construction categories like Sets.Infinite or
Sets.CartesianProducts. It's not clear whether it should include
specialized categories like

sage.combinat.ncsf_qsym.generic_basis_code.BasesOfQSymOrNCSF

an_instance should be made to work at least for the categories
discovered by category_sample, and possibly more::

sage: Sets.CartesianProducts.an_instance()
...
TypeError: __init__() takes at least 2 arguments (1 given)

CC: @simon-king-jena

Component: categories

Issue created by migration from https://trac.sagemath.org/ticket/15696

[nthiery]

comment:4

Attachment: all_categories.py.gz

Just for the record, I attach here a quick hack I did for my PyCon15 lightning talk to extract a graph of categories, by recursively extracting the functorial construction and axiom categories out of the main categories.

Progress note by the way: thanks to #18174, an_instance now works for most functorial constructions:

sage: Modules.Graded.an_instance()
Category of graded modules over Rational Field