#10667: Morphisms and Objects of Categories
---------------------------+------------------------------------------------
Reporter: SimonKing | Owner: nthiery
Type: enhancement | Status: new
Priority: major | Milestone:
Component: categories | Keywords: objects morphisms containment
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Comment(by SimonKing):
If a category has not its own implementation of a hom-category, currently
the join of the hom-categories of its super-categories is chosen. Hence,
we have
{{{
sage: CommutativeRings().hom_category()
Category of hom sets in Category of rings
sage: WeylGroups().hom_category()
Category of hom sets in Category of sets
}}}
I don't like that. One problem is that, for test suites, one would like to
have a sample object -- but there is no way to create a sample object for
a join of arbitrary categories.
Moreover, the "hom sets in the Category of rings" are simply wrong for the
category of ''commutative'' rings.
Instead, I suggest to walk through the list of all super categories of
`self`, take the first that has the attribute `HomCategory` (i.e., has a
custom implementation of a hom category), and insert `self` as argument
for that `HomCategory`:
{{{
sage: HopfAlgebrasWithBasis(QQ).hom_category()
Category of hom sets in Category of hopf algebras with basis over Rational
Field
sage: WeylGroups().hom_category()
Category of hom sets in Category of weyl groups
sage: type(HopfAlgebrasWithBasis(QQ).hom_category())
<class 'sage.categories.modules_with_basis.ModulesWithBasis.HomCategory'>
sage: type(WeylGroups().hom_category())
<class 'sage.categories.sets_cat.Sets.HomCategory'>
}}}
Of course, it may happen that several super categories have different
custom implementation of hom categories, and we pick just one. But I think
this should be taken care of manually, as join categories have a serious
drawback, IMHO.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10667#comment:1>
Sage <http://www.sagemath.org>
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