Corollary 7.2.8.9. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. Then $\operatorname{\mathcal{C}}$ is sifted if and only if it is nonempty and, for every pair of objects $X,Y \in \operatorname{\mathcal{C}}$, the $\infty $-category $\operatorname{\mathcal{C}}_{X/} \times _{\operatorname{\mathcal{C}}} \operatorname{\mathcal{C}}_{Y/}$ is weakly contractible.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$