Corollary 7.3.5.11. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category which has an initial object and let $U: \operatorname{\mathcal{D}}\rightarrow \operatorname{\mathcal{E}}$ be a cocartesian fibration of $\infty $-categories. Then every lifting problem
\[ \xymatrix@R =50pt@C=50pt{ \operatorname{\mathcal{C}}^{\mathrm{init}} \ar [r]^-{F_0} \ar [d] & \operatorname{\mathcal{D}}\ar [d]^{U} \\ \operatorname{\mathcal{C}}\ar [r]^-{G} \ar@ {-->}[ur]^{F} & \operatorname{\mathcal{E}}} \]
admits a solution $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ which is $U$-left Kan extended from the full subcategory $\operatorname{\mathcal{C}}^{\mathrm{init}} \subseteq \operatorname{\mathcal{C}}$ spanned by the initial objects.