Theorem 9.4.0.2. Let $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ be an essentially small inner fibration of $\infty $-categories. Then there exists a commutative diagram
\[ \xymatrix@R =50pt@C=50pt{ \operatorname{\mathcal{E}}\ar [rr]^-{H} \ar [dr]_{U} & & \widehat{\operatorname{\mathcal{E}}} \ar [dl]^{ \widehat{U} } \\ & \operatorname{\mathcal{C}}& } \]
which exhibits $\widehat{\operatorname{\mathcal{E}}}$ as a fiberwise cocompletion of $\operatorname{\mathcal{E}}$. Moreover, the inner fibration $\widehat{U}$ is unique up to equivalence.