Remark 4.3.3.18. Let $i: X \hookrightarrow X'$ and $j: Y \hookrightarrow Y'$ be monomorphisms of simplicial sets. From the description of Remark 4.3.3.17, we see that the join $(i \star j): X \star Y \rightarrow X' \star Y'$ is also a monomorphism of simplicial sets.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$