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. ThiƩry "Isil" <nthi...@users.sf.net> http://Nicolas.Thiery.name/ --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "sage-combinat-devel" group. To post to this group, send email to sage-combinat-devel@googlegroups.com To unsubscribe from this group, send email to sage-combinat-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-combinat-devel?hl=en -~----------~----~----~----~------~----~------~--~---