On a (terminally connected, pro-etale) factorization of geometric morphisms
Category Theory
2025-02-07 v1
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.
Cite
@article{arxiv.2502.04213,
title = {On a (terminally connected, pro-etale) factorization of geometric morphisms},
author = {Olivia Caramello and Axel Osmond},
journal= {arXiv preprint arXiv:2502.04213},
year = {2025}
}
Comments
39 pages