Definition 99.12.3. Let $S$ be a scheme. Let $\mathcal{X}$ be a locally Noetherian algebraic stack over $S$. The *dimension* $\dim (\mathcal{X})$ of $\mathcal{X}$ is defined to be

\[ \dim (\mathcal{X}) = \sup \nolimits _{x \in |\mathcal{X}|} \dim _ x(\mathcal{X}) \]

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