#17359: Hom sets for schemes and Hecke modules
-------------------------------------+-------------------------------------
Reporter: pbruin | Owner:
Type: defect | Status: needs_review
Priority: minor | Milestone: sage-6.5
Component: categories | Resolution:
Keywords: hecke module | Merged in:
scheme homset | Reviewers:
Authors: Peter Bruin | Work issues:
Report Upstream: N/A | Commit:
Branch: | b6699929d45a09eb233f61e7e9c1b2c57f7cdf1c
u/pbruin/17359-homsets_schemes_hecke_modules| Stopgaps:
Dependencies: #17364 |
-------------------------------------+-------------------------------------
Changes (by pbruin):
* keywords: scheme homset => hecke module scheme homset
* commit: => b6699929d45a09eb233f61e7e9c1b2c57f7cdf1c
* status: needs_work => needs_review
* branch: => u/pbruin/17359-homsets_schemes_hecke_modules
Old description:
> In #17364, the supercategories of homsets of schemes were fixed: instead
> of
> {{{
> sage: Schemes().Homsets().all_super_categories()
> [Category of homsets of schemes, Category of objects]
> }}}
> we now have
> {{{
> sage: Schemes().Homsets().all_super_categories()
> [Category of homsets of schemes,
> Category of homsets,
> Category of sets,
> Category of sets with partial maps,
> Category of objects]
> }}}
> There are two TODO items left from #17364, namely to determine the
> correct categories for homsets of schemes and of Hecke modules. The
> purpose of this ticket is to resolve these TODOs.
New description:
In #17364, the supercategories of homsets of schemes were fixed: instead
of
{{{
sage: Schemes().Homsets().all_super_categories()
[Category of homsets of schemes, Category of objects]
}}}
we now have
{{{
sage: Schemes().Homsets().all_super_categories()
[Category of homsets of schemes,
Category of homsets,
Category of sets,
Category of sets with partial maps,
Category of objects]
}}}
There are two TODO items left from #17364, namely to determine the correct
categories for homsets of schemes and of Hecke modules. The purpose of
this ticket is to resolve these TODOs as follows:
- Hom sets of schemes are unchanged (do not have any extra structure)
- Hom sets of Hecke modules over a ring ''A'' are now in the category of
''A''-modules. (Note that `HeckeModules(A)` requires ''A'' to be
commutative, while Hecke algebras are not always commutative. Hence Hom
sets are modules over ''A'' but not in general over the Hecke algebra.)
--
--
Ticket URL: <http://trac.sagemath.org/ticket/17359#comment:8>
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