On a (terminally connected, pro-etale) factorization of geometric morphisms
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.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.