The Stacks project

Definition 101.17.1. Let $f : \mathcal{X} \to \mathcal{Y}$ be a morphism of algebraic stacks.

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

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