Proposition 9.4.6.22. Let $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ be a flat inner fibration of $\infty $-categories. Then $U$ factors as a composition $\operatorname{\mathcal{E}}\xrightarrow {F} \operatorname{\mathcal{E}}' \xrightarrow {U'} \operatorname{\mathcal{C}}$, where $F$ is an equivalence of $\infty $-categories and $U'$ is a flat isofibration. Moreover, for each object $C \in \operatorname{\mathcal{C}}$, the induced map $F_{C}: \operatorname{\mathcal{E}}_{C} \rightarrow \operatorname{\mathcal{E}}'_{C}$ is a Morita equivalence.
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