Corollary 7.3.5.2. Let $\operatorname{\mathcal{C}}$ and $\operatorname{\mathcal{D}}$ be $\infty $-categories and let $\delta : K \rightarrow \operatorname{\mathcal{C}}$ be a diagram. Assume that, for every object $C \in \operatorname{\mathcal{C}}$, the $\infty $-category $\operatorname{\mathcal{D}}$ admits $K_{/C}$-indexed colimits. Then every diagram $F_0: K \rightarrow \operatorname{\mathcal{D}}$ admits a left Kan extension along $\delta $.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$