Corollary 1.1.5.11. The construction $S \mapsto \underline{S}$ determines a fully faithful embedding $\operatorname{Set}\hookrightarrow \operatorname{Set_{\Delta }}$. The essential image of this embedding is the full subcategory of $\operatorname{Set_{\Delta }}$ spanned by the discrete simplicial sets.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$