Corollary 9.4.6.26. Let $U_0: \operatorname{\mathcal{E}}_0 \rightarrow \operatorname{\mathcal{C}}_0$ be a flat inner fibration of simplicial sets. Then there exists a pullback diagram
\[ \xymatrix@R =50pt@C=50pt{ \operatorname{\mathcal{E}}_0 \ar [r] \ar [d]^{U_0} & \operatorname{\mathcal{E}}\ar [d]^{U} \\ \operatorname{\mathcal{C}}_0 \ar [r]^-{\iota } & \operatorname{\mathcal{C}}, } \]
where $U$ is a flat inner fibration of $\infty $-categories. Moreover, we may assume that $\iota $ is inner anodyne.