As far ar I see, the problem is only the problem of set theory. If we allow the class of all classes, we run into Russell's paradox. If we use a theory lihe ZFC with the additional axiom that every set is a member of a Grothendieck universe (or - equvivalently - for every cardinal c there exists a strongly inaccessible cardinal larger than c) then the category of all functors from some category in a universe U to the category of all sets in U is a topos in the next universe U^+. If this presheaf category or the category of sheaves for a given site in U has a skeleton in U, then this skeleton is a sheaf in U. If one tries to build up a mathematics based on topos theory without any reference to an "outside world of sets", I do not see what "large site" means. Greetings Reinhard- 22-Jun-2002 11:19:26 -0300,5457;000000000000-00000000