The Stacks project

Definition 100.7.5. Let $\mathcal{P}$ be a property of germs of schemes which is smooth local. Let $\mathcal{X}$ be an algebraic stack. Let $x \in |\mathcal{X}|$. We say $\mathcal{X}$ has property $\mathcal{P}$ at $x$ if any of the equivalent conditions of Lemma 100.7.4 holds.

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