The \'Etale Fundamental Groupoid as a Terminal Costack

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