Example 7.3.3.5. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ and $U: \operatorname{\mathcal{D}}\rightarrow \operatorname{\mathcal{E}}$ be functors of $\infty $-categories. If $U$ is fully faithful, then $F$ is $U$-left Kan extended and $U$-right Kan extended from any full subcategory $\operatorname{\mathcal{C}}^{0} \subseteq \operatorname{\mathcal{C}}$ (see Example 7.1.6.4).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$