#17364: Homset categories should be subcategories of the category of all homsets
-------------------------------------+-------------------------------------
Reporter: nthiery | Owner:
Type: defect | Status: needs_review
Priority: major | Milestone: sage-6.5
Component: categories | Resolution:
Keywords: | Merged in:
Authors: Nicolas M. Thiéry | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/nthiery/all_homsets_category_should_be_subcategories_of_the_category_of_all_homsets|
0925390c0d1eacabd75bb24c815d30124c8e8a2b
Dependencies: | Stopgaps:
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Old description:
> All homsets category should be subcategories of the category of all
> homsets. For example, we want:
> {{{
> sage: from sage.categories.homsets import Homsets
> sage: Schemes().Homsets().is_subcategory(Homsets())
> True
> sage: AdditiveMagmas().Homsets().is_subcategory(Homsets())
> True
> sage:
> AdditiveMagmas().AdditiveUnital().Homsets().is_subcategory(Homsets())
> True
> }}}
>
> The inheritance of an homset category ``C.Homsets()`` from
> ``Homsets()`` used to be implemented in
> ``HomsetsCategory.extra_super_categories``; this meant that any custom
> implementation of ``C.Homsets.extra_super_categories`` would overwrite
> it, which broke all the above examples.
>
> This ticket fixes this, and uses the occasion to refactor the logic,
> getting rid along the way of the custom ``category_of`` method which
> almost duplicated that of functorial constructions. Hopefully the
> logic and its the documentation, are clearer now.
New description:
All homset categories should be subcategories of the category of all
homsets. For example, we want:
{{{
sage: from sage.categories.homsets import Homsets
sage: Schemes().Homsets().is_subcategory(Homsets())
True
sage: AdditiveMagmas().Homsets().is_subcategory(Homsets())
True
sage:
AdditiveMagmas().AdditiveUnital().Homsets().is_subcategory(Homsets())
True
}}}
The inheritance of a homset category `C.Homsets()` from `Homsets()` used
to be implemented in `HomsetsCategory.extra_super_categories`; this meant
that any custom implementation of `C.Homsets.extra_super_categories` would
overwrite it, which broke all the above examples.
This ticket fixes this, and uses the occasion to refactor the logic,
getting rid along the way of the custom `category_of` method which almost
duplicated that of functorial constructions. Hopefully the logic and its
documentation are clearer now.
--
Comment (by pbruin):
(just fixing some typos in the description and summary)
Replying to [comment:4 nthiery]:
> There remains one thing: what to do with `Schemes.Homsets` and
`HeckeModules.Homsets`? Probably fine as they are without
`extra_super_categories`. My tiny changes there are likely to conflict
with those in #17359. Please take over, and feel free too edit that part,
and make either ticket depend on the other.
In that case I propose using #17359 to finish the two `TODO` items from
this ticket (for Hecke modules and schemes).
--
Ticket URL: <http://trac.sagemath.org/ticket/17364#comment:6>
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