Remark 10.3.1.3 (Base Change). Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a morphism of simplicial sets, and let $\operatorname{\mathcal{D}}^{0} \subseteq \operatorname{\mathcal{D}}$ be a sieve on $\operatorname{\mathcal{D}}$. Then the inverse image $\operatorname{\mathcal{C}}^{0} = F^{-1}( \operatorname{\mathcal{D}}^{0} )$ is a sieve on $\operatorname{\mathcal{C}}$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$