#10963: More functorial constructions
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Reporter: nthiery | Owner: stumpc5
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.1
Component: categories | Resolution:
Keywords: days54 | Merged in:
Authors: Nicolas M. Thiéry | Reviewers: Simon King, Frédéric
Report Upstream: N/A | Chapoton
Branch: | Work issues:
public/ticket/10963 | Commit:
Dependencies: #11224, #8327, | 8045aa4a4b7ada735b3eb6055382f9b341a39f1e
#10193, #12895, #14516, #14722, | Stopgaps:
#13589, #14471, #15069, #15094, |
#11688, #13394, #15150, #15506 |
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Comment (by vbraun):
Replying to [comment:405 nbruin]:
> There's a peculiarity in this representation of the concept: with this
paradigm
> it would be possible to implement multiple `axiom.Finite` subclasses on
> `Cs`.
Yes, giving you additional freedom to only implement methods when certain
combinations of axioms are applied:
{{{
class Cs(Category):
....: class WithFoo(Foo):
....: class ParentMethods:
....: def foo(self): [...]
....: class WithBar(Bar):
....: class ParentMethods:
....: def bar(self): [...]
....: class WithFooAndBar(Foo, Bar):
....: class ParentMethods:
....: def baz(self): [...]
}}}
> I wonder if "name clashes" in axioms are ever a real problem.
Funny that you would say that, as Atiyah's category of "Real" vector
bundles would be another example of a likely name clash with what you'd
commonly use "Real" for.
> I would hope that
> if two categories `A` and `B` have conflicting ideas over what the axiom
> named `d` must mean, then any common supercategory doesn't implement
either
Yes, I'm aware that you could use the same adjective provide that they are
not joined by a common supercategory. It seems a bit fragile as adding new
supercategories may then have very non-local consequences. Moreover, for
differential operators, say, I think it would be possible (if highly
unusual) to ask them to form a "Rigid" category. So they can't be
separated by not having a common supercategory, at least not in a
mathematically satisfying way.
--
Ticket URL: <http://trac.sagemath.org/ticket/10963#comment:406>
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