#10963: Axioms and more functorial constructions
-------------------------------------+-------------------------------------
Reporter: nthiery | Owner: stumpc5
Type: enhancement | Status: needs_info
Priority: major | Milestone: sage-6.2
Component: categories | Resolution:
Keywords: days54 | Merged in:
Authors: Nicolas M. Thiéry | Reviewers: Simon King, Frédéric
Report Upstream: N/A | Chapoton
Branch: | Work issues: merge with #15801
public/ticket/10963-doc- | once things stabilize
distributive | Commit:
Dependencies: #11224, #8327, | ce2193e9d6f179d2d51812c6af002697ccfbaa8c
#10193, #12895, #14516, #14722, | Stopgaps:
#13589, #14471, #15069, #15094, |
#11688, #13394, #15150, #15506, |
#15757, #15759, #15919 |
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Comment (by nthiery):
Replying to [comment:617 darij]:
> I've just pushed a merge to make the branch green again.
Thanks.
> Just to doublecheck, removing the `cardinality` method in
`src/sage/categories/enumerated_sets.py` was intention, right?
More precisely it was intentionally moved up to sets.py. Thanks for
double checking though!
> Thanks for the reference to the doc of `Subquotients`; that said,
`Quotients` as well (and maybe even more so) needs documentation.
Isn't the cross-reference to Subquotients enough? I'd like to avoid
duplicating the detailed explanations there. I have added a ``(in fact
homomorphic image)'' in Quotients to be more specific though.
> (There is a typo in the doc of `Subquotients` btw: the two `\mapsto`
signs should be `\to` signs.
Fixed. Thanks!
> And the maps `l` and `r` shouldn't be called structure-preserving; in
usual cases, only `r` is structure-preserving (and this is precisely what
that equation says).
Right; it can be confusing to think of `l` as structure preserving. I
changed the phrase to only state that `r` is structure
preserving. It's not perfect though, as we don't want to require `r`
to be a morphism (if not just because B' might not even be a
subobject), and the specific definition of structure preserving which
is stated and is the one we need in practice is not just about r, but
about the pair r and l. Anyway, probably good enough for now.
> I'd fix these myself but I can't be assed to find the source file
containing the docstring -- just writing `Subquotients??` in the terminal
does not show me where the doc is located, which if you ask me is another
bug of our caching system.)
Yes that's annoying; this indeed pops back every now and then despite
all the hard work Simon has been putting on that. Typical workarounds I
use:
{{{
sage: C = Sets()
sage: C.Subquotients.f??
}}}
or:
{{{
sage: C.Subquotients.__module__
}}}
> I guess I can't really say if I am happy with `Quotients` before I know
how they are used. The documentation at least explains the purpose to me.
I think the subtleties will emerge when we start implementing (lowercase)
`quotient` methods to return actual quotients of parents; if we aren't
careful about distinguishing between different ground categories then, we
will run into trouble.
On the category side, the infrastructure is definitely meant to be
used by calling `C.Quotients()` to specify explicitly the ground
category `C`. That's what `quotient` methods should do; and, unless
there is no ambiguity from the input (e.g. a quotient of a polynomial
ring by an ideal), they should actually request `C` to the user.
Cheers,
Nicolas
--
Ticket URL: <http://trac.sagemath.org/ticket/10963#comment:630>
Sage <http://www.sagemath.org>
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