Corollary 9.1.4.19. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a right cofinal functor between filtered $\infty $-categories. Then, for every object $C \in \operatorname{\mathcal{C}}$, the induced map of coslice $\infty $-categories $F_{C/}: \operatorname{\mathcal{C}}_{C/} \rightarrow \operatorname{\mathcal{D}}_{ F(C)/ }$ is right cofinal.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
Proof. Apply Corollary 9.1.4.18 in the special case $\kappa = \aleph _0$ and $K = \Delta ^0$. $\square$