Are all finitely presentable Heyting pretoposes finite quotients of a free Heyting pretopos?

Determine whether every finitely presentable Heyting pretopos H (that is, every Heyting pretopos complete with respect to finite models on finite Kripke frames) is equivalent to a finite quotient of a free Heyting pretopos Hey[I] generated by some finite pretopos [I].

Background

The paper develops a stack representation for finitely presentable Heyting pretoposes, defined as those Heyting pretoposes that are complete with respect to finite models on finite Kripke frames. A central construction is the free Heyting pretopos Hey[I] generated by a finite pretopos [I], where [I] arises from a finite Cauchy complete category I via the presheaf topos [I, Set]. The authors note that typical examples of finitely presentable Heyting pretoposes include finite quotients of such free Heyting pretoposes.

Within Section 3.2, after showing that slices of finite Heyting pretoposes are again finite, the authors raise the classification question of whether every finitely presentable Heyting pretopos can be obtained as a finite quotient of some Hey[I]. This remains unresolved in the paper and is identified explicitly as an open point.