#10668: Refactor category support for morphisms (Hom is not a functorial
construction!)
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Reporter: nthiery | Owner: nthiery
Type: defect | Status: new
Priority: major | Milestone:
Component: categories | Keywords:
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Comment(by SimonKing):
Replying to [comment:2 nthiery]:
> Very short answer for now: here the question is whether Hom_Rings()(A,B)
is an object of Hom_Sets(). It's not. The point of
VectorSpaces().HomCategory() is to encode mathematical information about
the homsets, like the fact that Hom(A,B) is itself a vector space. We
don't want this information to be applied to a homset of a subcategory (a
homset in Algebras() being certainly not a vector space).
Right.
Nevertheless, I believe that an attribute like `C.hom_structure` would be
a convenient way to declare that the homsets of `C` all have a particular
structure (like `Rings()` or `VectorSpaces(C.base_ring())`) and that
therefore `C.hom_category()` is a sub-category of `C.hom_structure`.
So, for now, the only detail that I have to withdraw from my proposal is
that `C.hom_structure` will not be influenced by `X.hom_structure` for a
super-category `X` of `C`.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10668#comment:3>
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