On a (terminally connected, pro-etale) factorization of geometric morphisms

2025/02/06 by Caramello, Olivia, Osmond, Axel
#Category Theory (math.CT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2502.04213

Abstract

We extend the classical (connected, etale) factorization of locally connected geometric morphisms into a (terminally connected, pro-etale) factorization for all geometric morphisms between Grothendieck topoi. We discuss properties of both classes of morphisms, particularly the relation between pro-etale geometric morphisms and the category of global elements of their inverse image; we also discuss their stability properties as well as some fibrational aspects.

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