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arXiv · 2502.04213

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

Olivia Caramello·Axel Osmond
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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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Olivia Caramello, Axel Osmond. 2025-02-06. On a (terminally connected, pro-etale) factorization of geometric morphisms. https://arxiv.org/abs/2502.04213

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