# Exodromy for stacks

## TL;DR

This paper extends the Exodromy Theorem to a broader class of stacks and higher stacks by generalizing the Galois category construction to simplicial schemes, linking it to their étale topological type.

## Contribution

It generalizes the Exodromy Theorem to higher stacks and simplicial schemes, connecting Galois categories with étale topological types.

## Key findings

- Galois category construction extended to simplicial schemes
- Nerve of Galois category equivalent to étale topological type
- Broader applicability of Exodromy Theorem to stacks

## Abstract

In this short note we extend the Exodromy Theorem of arXiv:1807.03281 to a large class of stacks and higher stacks. We accomplish this by extending the Galois category construction to simplicial schemes. We also deduce that the nerve of the Galois category of a simplicial scheme is equivalent to its \'etale topological type in the sense of Friedlander.