Explain category: autogenerated overview documentation of a category

[nthiery]

The purpose of this ticket is to complement the static documentation
of a category by an autogenerated overview of it including:

• a description of the category taken from its docstring (if there is one)

• the list of the important super categories (e.g. the result of
  super_structure_categories of Infrastructure for modelling full subcategories #16340)

• the list of the axioms

• the list of all the methods on parents, elements, ..., including the
  _test_*, _*_ and __**__ methods. For each method, there would
  be a short description (taken from the docstring), and information
  on where the method is defined (e.g. as an abstract method) and
  implemented.

• ???

This feature would be particularly useful for categories with axioms
or functorial construction categories since in most case this would
provide complete information without having to write any static
documentation.

Possible user interface to access the documentation

• Make it available with C?; this would require some magic to
  automagically replace the static documentation

• Add an explain_category method

• Use IPython's %pinfo/%pinfo2/help infrastructure

CC: @sagetrac-sage-combinat @hivert @simon-king-jena @darijgr @nbruin @pjbruin @vbraun

Component: categories

Keywords: days57

Issue created by migration from https://trac.sagemath.org/ticket/16363

[nthiery]

Changed keywords from none to days57

[nthiery]

comment:1

This was suggested by Volker at Sage Days 57