The Stacks project

Definition 58.6.1. Let $X$ be a connected scheme. Let $\overline{x}$ be a geometric point of $X$. The fundamental group of $X$ with base point $\overline{x}$ is the group

of automorphisms of the fibre functor $F_{\overline{x}} : \textit{FÉt}_ X \to \textit{Sets}$ endowed with its canonical profinite topology from Lemma 58.3.1.