English

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.

Keywords

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

R2 v1 2026-06-28T21:35:01.556Z