flat topologies

["Szlachanyi Kornel" <szlach@rmki.kfki.hu>]

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

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Kornel Szlachanyi
Research Institute for Particle and Nuclear Physics
of the Hungarian Academy of Science
Budapest
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