#10963: More functorial constructions
-------------------------------------+-------------------------------------
Reporter: nthiery | Owner: stumpc5
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.1
Component: categories | Resolution:
Keywords: days54 | Merged in:
Authors: Nicolas M. Thiéry | Reviewers: Simon King, Frédéric
Report Upstream: N/A | Chapoton
Branch: | Work issues:
public/ticket/10963 | Commit:
Dependencies: #11224, #8327, | eb7b486c6fecac296052f980788e15e2ad1b59e4
#10193, #12895, #14516, #14722, | Stopgaps:
#13589, #14471, #15069, #15094, |
#11688, #13394, #15150, #15506 |
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Comment (by nthiery):
Some good news:
- There actually is an easy workaround for implementing axioms like
Distributive whose highest category class is a join. Now I can do:
{{{
sage: (CommutativeAdditiveGroups() & Monoids()).Distributive()
Category of rings
}}}
It's not perfect though. The caveats are described in the
documentation: two are really minor, one a bit more annoying. But at
least it implements the above very natural notation right now until
a better solution is found!
- The (sketch of) proof of the infrastructure is finished.
A nice feature is that the specifications were actually more
stringent than necessary, as I first found out while searching for
counter examples:
It actually would be very well possible to implement {{{FiniteFields}}}
as
{{{DivisionRings.Finite}}} rather than as {{{Fields.Finite}}}!
The infinite recursions I was previously getting were apparently
just due to caveats in earlier implementations. With that, we could
possibly get rid of the ``A_extra_super_categories`` hook mechanism;
however this mechanism brings more flexibility in the organization
of the code, so I'd rather keep it.
- The axiom documentation should be rather complete and in particular
include discussions for all the points that were raised recently on
the ticket.
Pushed to u/nthiery/ticket/10963 and compiled doc on [1], as usual.
Please check out and review!
Cheers,
Nicolas
[1]
http://sage.math.washington.edu/home/nthiery/sage-6.0/src/doc/output/html/en/reference/categories/sage/categories/category_with_axiom.html
--
Ticket URL: <http://trac.sagemath.org/ticket/10963#comment:481>
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