Appears in collection : Toposes Online

We explore criteria for the axiomatizability of images of functors by kappa-geometric sequents. We observe that under mild hypotheses functors between accessible categories can be assumed to be induced by a kappa-geometric morphism between classifying kappa-toposes, and we arrive at our criteria using the factorization of this morphism into a surjection, followed by a dense inclusion, followed by a closed inclusion.