The Stacks project

Definition 101.23.2. Let $f : \mathcal{X} \to \mathcal{Y}$ be a morphism of algebraic stacks. We say $f$ is locally quasi-finite if $f$ is quasi-DM, locally of finite type, and for every morphism $\mathop{\mathrm{Spec}}(k) \to \mathcal{Y}$ where $k$ is a field the space $|\mathcal{X}_ k|$ is discrete.