#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 nthiery):
Replying to [comment:54 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.
We do not even want to construct it on the fly! FiniteFields satisfies
at least four axioms that can apply to Magmas (Associative, Finite,
Unital, Commutative). We do not want the category hierarchy above
FiniteFields to contain {2^4} categories (most of which being trivial)
just for Magmas.
And that many for additive magmas.
> 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()`.
Note that this is currently resolved automatically by the current
mechanism by looking which axioms are defined/implemented by the
various categories.
> 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().Commutative().Finite() in
Fields().Finite().all_super_categories()
> False
> }}}
> even though
> {{{
> sage: (Fields().Finite()).is_subcategory(Rings().Commutative().Finite())
> True
> }}}
Which is exactly what I want since finite commutative rings is
trivial, and realized as a join category. There is no point in adding
join categories in all_super_categories.
Cheers,
Nicolas
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10963#comment:56>
Sage <http://www.sagemath.org>
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