#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:617 darij]:
> 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.
I strongly support your opinion. An example that annoys me a lot (already
present before this ticket) is
{{{
sage: C = Sets(); D = Groups()
sage: D.is_subcategory(C)
True # expected False
}}}
In my humble opinion, either this should return `False`, or the name
`is_subcategory()` should be changed so that it does not go against the
established meaning of the notion of subcategory. I would be much happier
if the syntax would be something like `C.has_coerce_functor_from(D)` or
`D.has_coerce_functor_to(C)`. (This is just a first idea that came to
mind, suggested by `has_coerce_map_from()` for parents, but maybe the
analogy is not strong enough for that.)
--
Ticket URL: <http://trac.sagemath.org/ticket/10963#comment:619>
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