Remark 2.4.2.17. Let $\operatorname{\mathcal{C}}$ be a topologically enriched category, and let $\operatorname{\mathcal{C}}_{\bullet }$ denote the associated simplicial category (Example 2.4.2.16). Then $\operatorname{\mathcal{C}}_{\bullet }$ is locally Kan (since the singular simplicial set $\operatorname{Sing}_{\bullet }(X)$ of any topological space $X$ is a Kan complex; see Proposition 1.2.5.8).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$