I recently came across Benabou's paper in J Sym Logic on this topic. I couldn't find any further papers/books by him on this on MathSciNet. In particular the promised book doesn't seem to have appeared in print. I am curious if any further work has been done on this. While on foundations, (and relating specifically to categories of fractions) what kind of "equality" do we need? It would seem that if "extentional" equality is unnecessary, then superclasses/universes are not needed for categories of frations. [And one of Feferman's proposals gives up extentional equality anyway.] Of course, I realize that at this generality this ties in with weak categories etc, but what about things that are more rigid? Nath Rao 740-366-9341 rao.3@osu.edu It is the man, not the method, that solves the problem. (attributed to Poincare by E. T. Bell)