#10963: More functorial constructions
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Reporter: nthiery |
Owner: stumpc5
Type: enhancement |
Status: needs_work
Priority: major |
Milestone:
Component: categories |
Resolution:
Keywords: |
Work issues: Reduce startup time by 5%. Avoid "recursion depth exceeded
(ignored)". Trivial doctest fixes.
Report Upstream: N/A |
Reviewers: Simon King
Authors: Nicolas M. Thiéry |
Merged in:
Dependencies: #11224, #8327, #10193, #12895, #14516, #14722, #13589 |
Stopgaps:
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Comment (by SimonKing):
Replying to [comment:53 nthiery]:
>
> But this would mean constructing a trivial category for finite
commutative rings (there is currently no category code for finite
commutative rings).
That's the point: In my approach, this category would be constructed on
the fly, by means of a dynamic construction.
> Besides: should this be finite commutative rings? Or finite domains? Or
finite euclidean rings? ...
To be discussed. In the end of the day, this is a matter of what axioms we
have for fields that do not hold for all division rings, and which are
thus implied by adding `Finite()` to `Rings().Division()`.
However, I do think that the category of finite commutative rings should
be a super-category of the category of finite fields. But (with your
patch):
{{{
sage: Rings().Finite() in Fields().Finite().all_super_categories()
False
}}}
even though
{{{
sage: (Fields().Finite()).is_subcategory(Rings().Finite())
True
}}}
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10963#comment:54>
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