#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:621 pbruin]:
> In short, "groups are sets" is only true in the loose sense that there
is a forgetful functor '''Groups''' -> '''Sets''' (sending ''G'' to ''S''
in the above notation), not that this functor is a subcategory relation.
OK, now I get it (hopefully). The forgetful functor is not injective.
So, how to implement it? We want that `Groups().parent_class` is derived
from `Sets().parent_class` since there is a forgetful functor, but we want
that `Groups()` is not a subcategory of `Sets()`.
--
Ticket URL: <http://trac.sagemath.org/ticket/10963#comment:622>
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