Change of base for locally internal categories (Q1824681)

This paper is a continuation of the author's programme [see the preceding review, Zbl 0683.18003] of regarding locally internal categories over a topos \({\mathcal E}\) as categories enriched over the bicategory of spans in \({\mathcal E}\). In this paper he considers the effect of change of base along a geometric morphism p: \({\mathcal F}\to {\mathcal E}:\) in particular, he obtains a result from which R. Diaconescu's well-known characterization of geometric morphisms into a topos of the form \({\mathcal E}^ C\) may be deduced as an easy corollary.