#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: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. Maybe one would use "implemented in Sage" rather than
"constructible in Sage" to rule out join categories.
(a short rephrasing is that super_cartegories give the covering
relations in the poset of implemented categories in Sage).
The only difference after this ticket is that there is a new syntax to
implement a category, e.g. {{{Blahs().Finite()}}}, as:
{{{
class Blahs(Category):
class Finite(CategoryWithAxiom):
}}}
but that's not really different from what we were already doing for
e.g. {{{Blahs().CartesianProducts()}}}.
> The problem with this old meaning of `C.super_categories()` is, of
> course, that "constructible in Sage" is a moving target, and hence
> it won't scale.
Let me rephrase this as: since "constructible in Sage" is a moving
target, maintaining by hand the information in super_categories()
often does not scale. So whenever possible, {{{super_categories}}}
should be calculated automatically.
Cheers,
Nicolas
--
Ticket URL: <http://trac.sagemath.org/ticket/10963#comment:64>
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