Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Example 7.3.3.8. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $U: \operatorname{\mathcal{D}}\rightarrow \operatorname{\mathcal{E}}$ be a functor of $\infty $-categories. It follows from Proposition 7.3.3.5 that a functor $\overline{F}: \operatorname{\mathcal{C}}^{\triangleright } \rightarrow \operatorname{\mathcal{D}}$ is a $U$-colimit diagram (in the sense of Definition 7.1.5.1) if and only if it is $U$-left Kan extended from $\operatorname{\mathcal{C}}$.