The Étale Fundamental Groupoid as a Terminal Costack

Abstract

Let $X$ be a noetherian scheme. We denote by ${\Pi }_1(X)$ the fundamental groupoid. In this paper we prove that the assignments $U\mapsto {\Pi }_1(U)$ is the 2-terminal costack over the site of étale coverings of $X$.

References in corpus (1)

• Introduction to the language of stacks and gerbes