#10963: More functorial constructions
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Reporter: | Owner: stumpc5
nthiery | Status: needs_work
Type: | Milestone:
enhancement | Resolution:
Priority: major | Merged in:
Component: | Reviewers: Simon King
categories | Work issues: Reduce startup time by 5%. Avoid
Keywords: | "recursion depth exceeded (ignored)". Trivial
Authors: | doctest fixes.
Nicolas M. Thiéry | Dependencies: #11224, #8327, #10193, #12895,
Report Upstream: N/A | #14516, #14722, #13589
Branch: |
Stopgaps: |
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Comment (by nthiery):
Replying to [comment:67 SimonKing]:
> This totally surprises me now.
Hmm, it feels like there is a rolling confusion here :-) Trac
communication is not so easy!
> Back to the `Fields().Finite().super_categories()` example. I have
argued that we have a couple of axioms, and keeping all axioms but one
gives us a list that (after removing duplicates) gives us a list of super
categories that exactly follows the specification above. And in
comment:51, I have shown that this definition more or less forces us to
have `Fields().Finite().super_categories() = [Category of fields, Category
of finite commutative rings]`.
>
> And you argued against this answer (because of having 2^4^ many
additional "empty" categories in the list of all super categories). You
seemed to be in favour of `Fields().Finite().super_categories() =
[Category of fields, Category of finite enumerated sets]`.
Yes and no: I indeed don't want all 2^4 potential categories. But I do
want those that are *implemented* in Sage. In the current state, we
have no category implemented for finite commutative rings (in other
words, Rings().Commutative().Finite() is a join category), but we do
have one for finite monoids (in Monoids.Finite). Hence the current
answer:
{{{[Category of fields, Category of finite monoids]}}}
Cheers,
--
Ticket URL: <http://trac.sagemath.org/ticket/10963#comment:68>
Sage <http://www.sagemath.org>
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