When is Fam(E) a topos?

Others may have noticed a slight gap in what I wrote on Saturday, concerning the difference between toposes with set-indexed copowers and those with coproducts. If E has copowers then the functor Delta exists, but to prove that Fam(E) is equivalent to the topos obtained by glueing along it you need arbitrary coproducts. In fact these are necessary for Fam(E) to be cartesian closed; I now have a proof of this, but it's a bit too complicated to write out in ASCII. I plan to write it up as a short paper. Peter Johnstone [For admin and other information see: http://www.mta.ca/~cat-dist/ ]