On Sunday 20 September 2009 14:21:13 jim stasheff wrote:
What do you call it when you have one (small) category being a (full) subcategory of another , and every object in the big category is isomorphic to one in the small category ? This is the case for the category given by objects hom(S,A) ,and morphisms given by the equivalence relation hom(T,A) ,as a subcategory of stack(A) .
In Adámek, Herrlich and Strecker's book "The Joy of Cats", the small category is said to be an "isomorphism-dense" subcategory of the big category. I don't know how widespread this terminology is, though.
Is there an equivalence of categories ?
Yes. Whenever A is a full, isomorphism-dense subcategory of B, then the inclusion functor from A to B is an equivalence (Remark 4.10 in that book). -- Robin Adams <robin@cs.rhul.ac.uk> Royal Holloway, University of London [For admin and other information see: http://www.mta.ca/~cat-dist/ ]