Is there an accepted name or attribution by which to refer to the following well-known theorem?

If C is a small site, then the topos of sheaves on C is the classifying topos for flat cover-preserving functors out of C.

In the case when C has a trivial topology, the corresponding assertion for its presheaf topos is usually called Diaconescu's theorem. But I don't think I have ever seen a name given to the more general version.

Sketches of an Elephantand section 4.5 of Borceux'sHandbook of Categorical Algebra 3both agree with Mike. $\endgroup$ – Tom Leinster Jul 11 '11 at 4:56