Remark 3.5.3.11. In the situation of Proposition 3.5.3.10, it suffices to consider the special case where $S = \Delta ^ m$ is a standard simplex. This follows from Corollary 1.1.4.9, since any simplicial set can be realized as a colimit of simplices (Remark 1.1.3.13).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$