Definition 101.46.3. Let $\mathcal{X}$ be an algebraic stack satisfying the equivalent conditions of Lemma 101.46.1. We define the *normalization* of $\mathcal{X}$ as the morphism

\[ \nu : \mathcal{X}^\nu \longrightarrow \mathcal{X} \]

constructed in Lemma 101.46.2.

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