The \'Etale Fundamental Groupoid as a Terminal Costack
  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 \'etale coverings of $X$. 
Ilia Pirashvili
math.AG