Remark 5.1.1.7 (Products). Let $\{ q_ i: X_ i \rightarrow S_ i \} _{i \in I}$ be a collection of morphisms of simplicial sets. Set $X = \prod _{i \in I} X_ i$, let $e$ be an edge of $X$ corresponding to a collection $\{ e_ i \} _{i \in I}$ of edges of the simplicial sets $\{ X_ i \} _{i \in I}$. If each $e_ i$ is $q_ i$-cartesian, then $e$ is $q$-cartesian, where $q$ denotes the product morphism $X = \prod _{i \in I} X_ i \rightarrow \prod _{i \in I} S_ i$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$