= Diaconescu equivalence for geometric morphisms
{c}
{title2=$\operatorname{Geom}(\mathcal E,\operatorname{Sh}(\mathcal C,J))\simeq\operatorname{Flat}_J(\mathcal C,\mathcal E)$}
<Geometric morphisms> into a sheaf topos correspond to continuous <flat functors> from its <site> into the domain topos, with continuity meaning that covers become jointly epimorphic families. Pulling back sheafified representables gives the <functor>; the tensor construction gives the inverse image in the other direction. This representation theorem should not be confused with the separately named Diaconescu theorem about choice and excluded middle.
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