Dear Andr'e, you suggest to neglect the higher order aspect of toposes, i.e. when one has a got a site in a logos then one may form sheaves over this internal site. But the result will be neither cc nor have a soc if the base logos was or has not. But I think that geometric morphisms between toposes do makes sense as Marta suggests because they capture the notion of relative Groth. toposes. Don't you also find Set a bit of fiction which not even all set theorists would find unproblematic. After all modern set theory is about relativity of ZFC (since the advent of forcing). I am not against using it but it is just a "facon de parler" for an anonymous base topos about which we may make stronger assumptions whenever convenient. Thomas [For admin and other information see: http://www.mta.ca/~cat-dist/ ]