Grothendieck Galois theory and étale exodromy

Abstract

Finite étale covers of a connected scheme $X$ are parametrised by the étale fundamental group via the monodromy correspondence. This was generalised to an exodromy correspondence for constructible sheaves, first in the topological setting by MacPherson, Treumann, Lurie, and others, and recently also for étale and pro-étale sheaves by Barwick--Glasman--Haine and Wolf. The proof of the étale exodromy theorem is long and technical, using many new definitions and constructions in the $(\infty,2)$-category of $\infty$-topoi. This paper gives a quick proof of the étale exodromy theorem for constructible sheaves of sets (with respect to a fixed stratification), in the style of Grothendieck's Galois theory.