#10963: Axioms and more functorial constructions
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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 SimonKing):
Replying to [comment:619 pbruin]:
> 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 don't get what you mean. Are you arguing that groups aren't necessarily
sets? Sure, all what we need is an object G together with a (inversion)
morphism G->G and a (multiplication) morphism GxG->G.
Would it be difficult to fix that, by removing `Sets()` from the list of
super-categories in all places where it is not requested by mathematical
axioms? I don't think so.
But then, we must not forget that "parents" in Sage's notion are objects
in some category containing elements. In other words, parents *are* sets.
Hence, the category for each implemented group in Sage would then
necessarily change from `Groups()` to `Groups()&Sets()`.
--
Ticket URL: <http://trac.sagemath.org/ticket/10963#comment:620>
Sage <http://www.sagemath.org>
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