The "Galois Correspondence" for n-Stacks

TL;DR

This paper establishes a Galois correspondence-like functor for n-stacks, linking fundamental group actions on finite sets to finite étale Deligne-Mumford n-stacks over a scheme, extending classical Galois theory to higher stacks.

Contribution

It introduces an essentially surjective functor connecting n-stacks with fundamental group actions to finite étale Deligne-Mumford n-stacks, generalizing Galois correspondence to higher stacks.

Findings

Constructs a Galois-like functor for n-stacks.

Shows the functor is essentially surjective.

Extends classical Galois theory to higher categorical structures.

Abstract

We prove an essentially surjective Galois-correspondence-like functor for $n$-stacks. More specifically, it gives an essentially surjective functor from the $\infty$-category of $n$-stacks of finite sets with an action of the fundamental group of $X$ to the $\infty$-category of Deligne-Mumford $n$-stacks finite \'etale over a connected scheme $X$.