#17364: Homset categories should be subcategories of the category of all homsets
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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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Comment (by pbruin):
I am not sure that this ticket solves all difficulties with determining
the supercategories of Hom set categories. For example (both before and
after this ticket):
{{{
sage: HeckeModules(ZZ).is_subcategory(Modules(ZZ))
True
sage: Modules(ZZ).Homsets().all_super_categories()
[Category of homsets of modules over Integer Ring,
Category of modules over Integer Ring,
Category of bimodules over Integer Ring on the left and Integer Ring on
the right,
Category of right modules over Integer Ring,
Category of left modules over Integer Ring,
Category of commutative additive groups,
Category of additive groups,
Category of additive inverse additive unital additive magmas,
Category of commutative additive monoids,
Category of additive monoids,
Category of additive unital additive magmas,
Category of commutative additive semigroups,
Category of additive commutative additive magmas,
Category of additive semigroups,
Category of additive magmas,
Category of homsets of right modules over Integer Ring and left modules
over Integer Ring,
Category of homsets,
Category of sets,
Category of sets with partial maps,
Category of objects]
sage: HeckeModules(ZZ).Homsets().all_super_categories()
[Category of homsets of Hecke modules over Integer Ring,
Category of homsets,
Category of sets,
Category of sets with partial maps,
Category of objects]
}}}
Note that the fact that Hom sets of modules are Abelian groups is not
reflected in the output of the last command.
--
Ticket URL: <http://trac.sagemath.org/ticket/17364#comment:8>
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