#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:
public/categories/over-a-base- | 0397865de0a1b9636b7501f0d666f08473b148fb
ring-category-15801 | Stopgaps:
Dependencies: #10963 |
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Comment (by nthiery):
Replying to [comment:21 tscrim]:
> Until I make a group ring over a group ring.
What about:
{{{
Modules(Groups().Algebras(Groups().Algebras()))
}}}
> Actually, maybe a less contrived example of modules over `S = R[a,b] /
J` where `R = ZZ[x,y] / I` for some ideals `I, J`. There should be more
morphisms as `R` modules than as `S` modules. I think this could be a
general issue anytime we try to do extension of scalars (or I'm being
completely paranoid).
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>
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.
Cheers,
Nicolas
--
Ticket URL: <http://trac.sagemath.org/ticket/15801#comment:23>
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