#15801: Categories over a base ring category
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Reporter: nthiery | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.2
Component: categories | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
public/categories/over-a-base- | 0397865de0a1b9636b7501f0d666f08473b148fb
ring-category-15801 | Stopgaps:
Dependencies: #10963 |
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Comment (by tscrim):
Replying to [comment:23 nthiery]:
Okay, I'm happy as long as we're getting things like this:
> {{{
> Modules(Groups().Algebras(Groups().Algebras()))
> }}}
for things like `(QQ[G])[H]` where `G,H` are groups.
> One thing is that each module M in Sage has a distinguished "base ring".
> <digression>
> In particular, M can't be in {{{Modules(R)}}} and in {{{Modules(S)}}}
> simultaneously; this can be seen as a limitation of the current
> category framework; no other CAS found a good solution to that
> though
> </digression>
<digressing as well>This might improve as (if) we implement coercions
between categories.</digressing as well>
> So, if I have two modules M and N, Hom(M,N) actually depends on this
> distinguished base ring (they should have the same!).
>
> If I build M and N as R-modules, and M' and N' as S-modules, the fact
> that they all belong to the same category only means that the code to
> handle and compute the homsets will be the same, not that the homsets
> Hom(M,N) and Hom(M',N') themselves will be the same.
Ah, I see. You ''must'' construct new modules M' and N' in order to
consider morphisms as S-modules. I'm good with everything (conceptually).
Simon, Nils, (or anyone else,) did either of you verify Nicolas' above (or
have any objections)?
--
Ticket URL: <http://trac.sagemath.org/ticket/15801#comment:25>
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