#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, | feab04a37ffb764b885dcefb63bb4a926977cee7
#10193, #12895, #14516, #14722, | Stopgaps:
#13589, #14471, #15069, #15094, |
#11688, #13394, #15150, #15506, |
#15757, #15759, #15919 |
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Comment (by darij):
I've just pushed a merge to make the branch green again. Just to
doublecheck, removing the `cardinality` method in
`src/sage/categories/enumerated_sets.py` was intention, right?
Also, sorry for the long silence on this ticket, and thanks for your
replies.
Thanks for the reference to the doc of `Subquotients`; that said,
`Quotients` as well (and maybe even more so) needs documentation.
(There is a typo in the doc of `Subquotients` btw: the two `\mapsto` signs
should be `\to` signs. 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). 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.)
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.
I still disagree with the idea of having GradedLieAlgebras a subcategory
of LieAlgebras. "Sub" implies injectivity throughout mathematics;
forgetful functors are not injective. IMHO the whole point of speaking in
categories is to piggyback on existing mathematical intuition of the user.
This is completely against that intuition.
--
Ticket URL: <http://trac.sagemath.org/ticket/10963#comment:617>
Sage <http://www.sagemath.org>
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