Example 4.6.9.6. Let $\operatorname{\mathcal{C}}$ be an ordinary category containing objects $X_0, X_1, \ldots , X_ n$, which we also regard as objects of the $\infty $-category $\operatorname{N}_{\bullet }(\operatorname{\mathcal{C}})$. Then the restriction map
\[ \theta : \operatorname{Hom}_{\operatorname{N}_{\bullet }(\operatorname{\mathcal{C}})}(X_0, X_1, \cdots , X_ n) \rightarrow \prod _{i=1}^{n} \operatorname{Hom}_{\operatorname{N}_{\bullet }(\operatorname{\mathcal{C}})}(X_{i-1}, X_ i) \]
is an isomorphism of (discrete) simplicial sets.