#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 pbruin):
Replying to [comment:624 tscrim]:
> I don't think we should use ''any'' functor, but only forgetful functors
to derive additional structure. So I'd call the method
`has_forgetful_functor_to()` and use that to inherit structure. Moreover,
it would be a nice feature to have coerce maps between categories and I'd
use the normal mechanism of `_has_coerce_map_from_()` (since functors are
the morphisms in the category of [concrete] categories right?).
One problem with the terminology "forgetful functor" is that it is not a
well-defined notion; see [http://mathoverflow.net/questions/19405
/definition-of-forgetful-functor]. Moreover, one important example would
be the inclusion functor of a subcategory (in the mathematical sense),
which does not actually forget any structure. So I'm not sure
`has_forgetful_functor_to()` would be the best name. (Although I'm also
not terribly happy with my own idea of using the terminology of coercion
here.)
Anyway, as I wrote above, I agree that this belongs to a separate ticket.
--
Ticket URL: <http://trac.sagemath.org/ticket/10963#comment:628>
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