#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 SimonKing):
Replying to [comment:64 nthiery]:
> Replying to [comment:60 SimonKing]:
> > And a more general question we should answer: What is the semantics of
`super_categories()`?
> >
> > It used to be like this, if I understood correctly:
`C.super_categories()` should return a list of all categories `S1, S2,
...` constructible in Sage such that C is a proper sub-category of `S1,
S2, ...` and there is no category D '''constructible in Sage''' such that
C is a proper sub-category of D and D is a proper sub-category of any of
the `S1, S2, ...`.
>
> I very much like this definition, and think it's still perfectly up to
> date.
This totally surprises me now.
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]`.
Actually, this is why I came up with the other specification of
`C.super_categories()`. That's why it surprises me that you now say you
like this specification less.
--
Ticket URL: <http://trac.sagemath.org/ticket/10963#comment:67>
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