Dear List, I have some questions on flat functors and Grothendieck topologies. It is probably well-known that if F: C--> Set is a flat functor on a small category then there is a Grothendieck topology on C in which the covering sieves S on the object c consist of sets of arrows to c such that {Fs|s in S} is jointly epimorphic on Fc. 1. Could you tell me a reference for this statement? 2. Is there a characterization of Grothendieck topologies that arise in this way from a flat functor? (`flat topologies'?) 3. For what categories C will there be a flat functor inducing the canonical topology on C? Thank you for any help. Kornel --------------------------------------------------- Kornel Szlachanyi Research Institute for Particle and Nuclear Physics of the Hungarian Academy of Science Budapest --------------------------------------------------- [For admin and other information see: http://www.mta.ca/~cat-dist/ ]