Remark 5.1.1.8. Let $q: X \rightarrow S$ be a morphism of simplicial sets, let $X' \subseteq X$ be a full simplicial subset, and let $q' = q|_{X'}$. If $e$ is an edge of $X'$ which is $q$-cartesian when viewed as an edge of $X$, then it it is $q'$-cartesian. This follows by combining Remark 5.1.1.6 with Example 5.1.1.5.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$