Dear David, dear Robert,
On Mon, Oct 26, 2009 at 02:53:41PM -0700, David Kohel wrote:
> If I understand what existed and what is proposed,
(for short, and semantically speaking, the current Groupoid is exactly
what existed before)
> then I vote for the category Groupoids() and no arguments.
Ok. That also was my feeling. But now I realized that it's actually
Robert who wrote the category Groupoid, and it is used in the Action
functor.
Robert: what's your point of view? If you vote for keeping the
category Groupoid around, could you please review it?
http://combinat.sagemath.org/patches/file/tip/categories-categories-nt.patch
http://trac.sagemath.org/sage_trac/wiki/CategoriesCategoriesReview
> A standard definition of a groupoid in category theory is a category
> in which every morphism is an isomorphism. Thus it is possible that
> this was intended as a constructor for any such category (whose
> underlying objects are in some given set), but a multigraph would
> probably be a more precise input (and efficient representation).
Yep, at least in the finite or not too large case.
> But there are many categories which might turn out to
> be groupoids, and it is unlikely that one constructor
> would suffice for their study. One still needs functors
> between categories to represent their morphisms (in
> the category Groupoids() of all groupoids).
> Those groupoids which do have a concrete representation
> (e.g. as a multigraph) and morphisms between them
> provide sufficient motivation to create the category
> Groupoids. The fact that each of its objects can be
> viewed as a category is an approach that can be
> explored later (if someone wants to build an effective
> framework for functors, natural transformations, etc.).
> The original code was set up to give a framework for
> category theory to organize mathematical constructs.
> The new category framework should be modular and
> flexible enough to delete unnecessary categories, or
> add a new one and experiment with its morphisms
> of functors from certain core categories.
>
> At present a constructor of a specific category, which
> happens to be a groupoid, is more of a motivating
> example for what one should be able to do rather than
> a core part of the categories framework.
Thanks David for your feedback.
Cheers,
Nicolas
--
Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/
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