On morphisms of relative toposes

Published 31 Oct 2023 in math.AG and math.CT | (2310.20691v1)

Abstract: We systematically investigate the functors between sites which induce morphisms of relative toposes. In particualar, we establish a relative version of Diaconescu's theorem, characterizing the relative geometric morphisms towards a relative sheaf topos in terms of a notion of flat (equivalently, filtered) functor relative to the base topos.

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