The Galois Correspondence for n-Stacks

Abstract

We prove a Galois correspondence for $n$-stacks. It gives a correspondence between the $\infty$-category of Deligne-Mumford $n$-stacks finite \'etale over a connected scheme $X$ and the $\infty$-category of $n$-stacks of finite sets with an action of the fundamental group of $X$.