Remark 2.4.2.15. Let $\operatorname{\mathcal{C}}_{\bullet }$ be a simplicial category. Then $\operatorname{\mathcal{C}}_{\bullet }$ is locally Kan if and only if the conjugate simplicial category $\operatorname{\mathcal{C}}_{\bullet }^{\operatorname{c}}$ (Example 2.4.2.12) is locally Kan.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$