The Stacks project

Definition 101.27.1. Let $f : \mathcal{X} \to \mathcal{Y}$ be a morphism of algebraic stacks.

1. We say $f$ locally of finite presentation if the equivalent conditions of Lemma 101.16.1 hold with $\mathcal{P} = \text{locally of finite presentation}$.

2. We say $f$ is of finite presentation if it is locally of finite presentation, quasi-compact, and quasi-separated.