Corollary 9.1.4.16. Let $\operatorname{\mathcal{C}}$ be a filtered $\infty $-category. For every object $C \in \operatorname{\mathcal{C}}$, the forgetful functor $\operatorname{\mathcal{C}}_{C/} \rightarrow \operatorname{\mathcal{C}}$ is right cofinal.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
Proof. Apply Corollary 9.1.4.15 in the special case $\kappa = \aleph _0$ and $K = \Delta ^0$. $\square$