Definition 101.34.2. Let $\mathcal{P}$ be a property of morphisms of algebraic spaces which is étale-smooth local on the source-and-target. We say a DM morphism $f : \mathcal{X} \to \mathcal{Y}$ of algebraic stacks *has property $\mathcal{P}$* if the equivalent conditions of Lemma 101.16.1 hold.

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