Exercise 7.3.2.3. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor of $\infty $-categories and let $\operatorname{\mathcal{C}}^{0} \subseteq \operatorname{\mathcal{C}}$ be a full subcategory. Show that, for every object $C \in \operatorname{\mathcal{C}}^{0}$, the functor $F$ is both left and right Kan extended from $\operatorname{\mathcal{C}}^0$ at $C$. For a more general statement, see Proposition 7.3.3.7.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$