The Stacks project

Example 58.5.1. Let $k$ be an algebraically closed field and $X = \mathop{\mathrm{Spec}}(k)$. In this case $\textit{FÉt}_ X$ is equivalent to the category of finite sets. This works more generally when $k$ is separably algebraically closed. The reason is that a scheme étale over $k$ is the disjoint union of spectra of fields finite separable over $k$, see Morphisms, Lemma 29.36.7.