Corollary 9.2.5.17. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a left exact functor of $\infty $-categories. Then $F$ is right cofinal.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
Proof. For every object $D \in \operatorname{\mathcal{D}}$, Theorem 9.2.5.15 guarantees that the $\infty $-category $\widetilde{\operatorname{\mathcal{C}}} = \operatorname{\mathcal{C}}\times _{\operatorname{\mathcal{D}}} \operatorname{\mathcal{D}}_{D/}$ is cofiltered. In particular, $\widetilde{\operatorname{\mathcal{C}}}$ is weakly contractible (Proposition 9.1.1.15). Allowing the object $D$ to vary, we conclude that $F$ is right cofinal (Theorem 7.2.3.1). $\square$