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Categories: adds support for SubcategoryMethods #12895

@nthiery

Description

@nthiery

With this patch, a category can implement a nested class SubcategoryMethods that provides methods for all subcategories of this category (similar to ParentMethods that provides methods for all parents of all subcategories of this category).

This is implemented by updating the class of each category C, at the end of its initialization, to insert C.subcategory_class as superclass (like what is done for Parents and Elements).

This is a bit tricky, since the super_categories method needs to be called during the initialization.

The patch is under finalization on http://combinat.sagemath.org/patches/

Apply

Depends on #9138
Depends on #11900
Depends on #11943
Depends on #12875
Depends on #12876
Depends on #12877
Depends on #11935
Depends on #12894

CC: @sagetrac-sage-combinat @simon-king-jena

Component: categories

Author: Nicolas M. Thiéry

Reviewer: Simon King

Merged: sage-5.11.beta2

Issue created by migration from https://trac.sagemath.org/ticket/12895

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