Given a geometric morphism n:E->F between Grothendieck toposes (over, say, Set) E is both an F-indexed category and a Set-indexed category. There is the following change of base result for any small (i.e. internal to Set) category C: - The category of F-indexed functors p^*C->E is equivalent to the category of Set-indexed functors C->E (where the first E is as an F-indexed cat and the second as a Set-indexed cat). (And p:F->Set.) Is there anything published/known as to the naturality of this equivalence? It is easy to see that it is natural in functors on C; but I also think (a) that it may be natural with respect to filtred cocontinuous functors between inductive completions of C and (b) between filtered cocontinuous functors on E. Thanks for any thoughts on this technical question, Regards, Christopher Townsend (Open University).