#15801: Categories over a base ring category
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Reporter: nthiery | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.2
Component: categories | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: #10963 | Stopgaps:
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Comment (by nthiery):
Replying to [comment:5 SimonKing]:
> We want to build on top of #10963, right?
Definitely.
> Replying to [comment:4 nthiery]:
> I think `_make_named_class_key` would still be make sense: We need to
distinguish the element and parent classes of `Algebras(Fields())` from
`Algebras(Rings())`, but probably not from `Algebras(QuotientFields())`.
That would be for free if we make Algebras a functorial construction:
if a category, say {{{QuotientFields()}}}, says nothing about algebras
over itself, then {{{Algebras(QuotientFields())}}} will actually
return {{{Algebras(Fields())}}}.
> And in particular (when following your suggestion below) we would still
want that `Modules(GF(5))` and `Modules(GF(7))` have the same parent and
element classes.
Right, if we go the join way, we will need to handle the base case of
Modules and have a make_named_class_key mechanism there.
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Ticket URL: <http://trac.sagemath.org/ticket/15801#comment:7>
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