Remark 10.3.1.4 (Transitivity). Let $\operatorname{\mathcal{C}}$ be a simplicial set containing simplicial subsets $\operatorname{\mathcal{C}}^{1} \subseteq \operatorname{\mathcal{C}}^{0} \subseteq \operatorname{\mathcal{C}}$, where $\operatorname{\mathcal{C}}^0$ is a sieve on $\operatorname{\mathcal{C}}$. Then $\operatorname{\mathcal{C}}^1$ is a sieve on $\operatorname{\mathcal{C}}^0$ if and only if it is a sieve on $\operatorname{\mathcal{C}}$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$