Corollary 7.6.2.18. Let $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ be an essentially small left fibration of $\infty $-categories. Then a functor $\mathscr {F}: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{S}}$ is a covariant transport representation for $U$ (in the sense of Definition 5.6.5.1) if and only if it is a left Kan extension of the constant functor $\underline{ \Delta ^0 }_{\operatorname{\mathcal{E}}}$ along $U$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$