Definition 10.3.1.1. Let $\operatorname{\mathcal{C}}$ be a simplicial set. A sieve on $\operatorname{\mathcal{C}}$ is a simplicial subset $\operatorname{\mathcal{C}}^{0} \subseteq \operatorname{\mathcal{C}}$ for which the inclusion map $\operatorname{\mathcal{C}}^{0} \hookrightarrow \operatorname{\mathcal{C}}$ is a right fibration.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$