# Kerodon

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Definition 2.4.1.8. Let $\operatorname{\mathcal{C}}_{\bullet }$ be a simplicial category. We will say that $\operatorname{\mathcal{C}}_{\bullet }$ is locally Kan if, for every pair of objects $X,Y \in \operatorname{\mathcal{C}}_{\bullet }$, the simplicial set $\operatorname{Hom}_{\operatorname{\mathcal{C}}}(X,Y)_{\bullet }$ is a Kan complex (Definition 1.1.9.1).