Corollary 4.6.9.5. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category containing objects $X_0, X_1, \ldots , X_ n$. Then the restriction map
\[ \operatorname{Hom}_{\operatorname{\mathcal{C}}}(X_0, X_1, \cdots , X_ n) \rightarrow \prod _{i=1}^{n} \operatorname{Hom}_{\operatorname{\mathcal{C}}}(X_{i-1}, X_ i) \]
is a trivial Kan fibration of simplicial sets.