Kerodon

Example 4.6.9.2. Let $\operatorname{\mathcal{C}}$ be a simplicial set containing vertices $X_0$ and $X_1$. Then the simplicial set $\operatorname{Hom}_{\operatorname{\mathcal{C}}}(X_0, X_1)$ of Notation 4.6.9.1 agrees with the morphism space $\operatorname{Hom}_{\operatorname{\mathcal{C}}}(X_0, X_1)$ of Construction 4.6.1.1. In particular, if $\operatorname{\mathcal{C}}$ is an $\infty $-category, then $\operatorname{Hom}_{\operatorname{\mathcal{C}}}(X_0, X_1)$ is a Kan complex (Proposition 4.6.1.10).