Corollary 7.2.2.14. Suppose we are given lifting problem
7.12
\begin{equation} \begin{gathered}\label{equation:easy-relative-colimit-existence} \xymatrix@R =50pt@C=50pt{ \operatorname{\mathcal{C}}\ar [r]^-{ f } \ar [d] & \operatorname{\mathcal{D}}\ar [d]^{U} \\ \operatorname{\mathcal{C}}^{\triangleleft } \ar [r] \ar@ {-->}[ur]^{\overline{f}} & \operatorname{\mathcal{E}}, } \end{gathered} \end{equation}
where $\operatorname{\mathcal{C}}$ is an $\infty $-category and $U$ is a cartesian fibration of $\infty $-categories. If $\operatorname{\mathcal{C}}$ has a final object $C$, then (7.12) admits a solution $\overline{f}: \operatorname{\mathcal{C}}^{\triangleleft } \rightarrow \operatorname{\mathcal{D}}$ which is a $U$-limit diagram.