TITLE: What sheaf topoi classify: attribution request
QUESTION [7 upvotes]: 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.

REPLY [3 votes]: If the site has finite limits, then this can be found in SGA4 Proposition 4.9.4.