Hi Robert, On 28 Dez., 23:41, Robert Bradshaw <rober...@math.washington.edu> wrote: > > According to your post, it should be "A group action G x S rightarrow > > S is a functor from G (considered as a category) to the category of > > Morphisms of Sets", and in the code it should be > > Functor.__init__(self, Groupoid(G), S.category().hom_category()). > > Not quite. It is G considered as a category where the elements of G > are the morphisms and there only one object, so it is actually a > functor to the categories of sets.
I see. But is that category actually implemented in Sage? Apparently it is not Groupoid(G) (as one might expect from the code snippet above): sage: G = SymmetricGroup(5) sage: C = Groupoid(G) sage: G.random_element() in C.hom_category() False Shouldn't the last line return "True"? I'd like to provide both the categorical approach towards actions and the other approach: It would be up to the user what approach to use for a new action, and there should be a way to consider any action both as a functor and as a map, regardless how it was defined (see my post on sage-algebra). But before that is possible, it seems that one needs to provide a proper HomCategory for groupoids with a __contains__ method that relies on containment in the underlying set. Cheers, Simon -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
