Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), Category Theory (math.CT)

journal:

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date:

2023-10-30 16:00:00

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.