Definition 67.22.2. Let $S$ be a scheme. Let $\mathcal{P}$ be a property of morphisms of schemes which is étale local on the source-and-target. We say a morphism $f : X \to Y$ of algebraic spaces over $S$ *has property $\mathcal{P}$* if the equivalent conditions of Lemma 67.22.1 hold.

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