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 #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

[nthiery]

This was suggested by Volker at Sage Days 57