Definition 101.50.1. We say an algebraic stack \mathcal{X} is integral if it is reduced, decent, \mathcal{I}_\mathcal {X} \to \mathcal{X} is quasi-compact, and |\mathcal{X}| is irreducible.
Definition 101.50.1. We say an algebraic stack \mathcal{X} is integral if it is reduced, decent, \mathcal{I}_\mathcal {X} \to \mathcal{X} is quasi-compact, and |\mathcal{X}| is irreducible.
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