Definition 99.27.1. Let $f : \mathcal{X} \to \mathcal{Y}$ be a morphism of algebraic stacks.

We say $f$

*locally of finite presentation*if the equivalent conditions of Lemma 99.16.1 hold with $\mathcal{P} = \text{locally of finite presentation}$.We say $f$ is

*of finite presentation*if it is locally of finite presentation, quasi-compact, and quasi-separated.

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