Definition 100.7.2 (04YG)—The Stacks project

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Part 7: Algebraic Stacks
Chapter 100: Properties of Algebraic Stacks
Section 100.7: Properties of algebraic stacks defined by properties of schemes
Definition 100.7.2 (cite)

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Definition 100.7.2. Let $\mathcal{X}$ be an algebraic stack. Let $\mathcal{P}$ be a property of schemes which is local in the smooth topology. We say $\mathcal{X}$ has property $\mathcal{P}$ if any of the equivalent conditions of Lemma 100.7.1 hold.

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