I call a functor F, such that F is one-one and onto on objects, and F sends each hom(a,b) ONTO hom(Fa,Fb), a _cofaithful_ functor. I call it that because every functor has an essentially unique decomposition as a faithful functor, followed by a cofaithful one. The question is, what do YOU call this? I would like to use the standard terminology if there is one. Thanks, Bill Rowan ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ Subject: On UA-CAT Workshop at MSRI Note from moderator: The following was received as a typescript from Saunders Mac Lane, with a request to post it, so typographical errors are mine. He mentions that his e-mail does not work well, and I will forward a copy of any discussion which ensues here to him, but of course he can also be contacted directly by mail. Bob Rosebrugh +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++