In my reply to the question about large sites for toposes I made the WRONG claim that if Psh(C) is a topos then all slices of C are essentially small. As Peter Johnstone pointed out this is a sufficient condition and he asked me for an argument for the reverse direction. Alas, I couldn't find one but instead I came across the following counterexample. Let G be a large group (e.g. all permutations of the universe whose collection of non-fixpoints is small, see 1.96(10) of ``Cats & Alligators'') then Psh(G) is a locally small cocomplete topos although G is not even locally small. However, every slice of G is trivial. But if one takes for C the large group G augmented with a terminal object then Psh(C) is a locally small cocomplete topos, too, whereas C/1 is not essentially small. Thomas Streicher 27-Jun-2002 10:17:23 -0300,6734;000000000000-00000000