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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