Remark 9.3.2.10. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. The following conditions are equivalent:
The $\infty $-category $\operatorname{\mathcal{C}}$ is locally discrete.
The comparison map $\operatorname{\mathcal{C}}\rightarrow \operatorname{N}_{\bullet }( \mathrm{h} \mathit{\operatorname{\mathcal{C}}} )$ is a trivial Kan fibration.
There exists an ordinary category $\operatorname{\mathcal{C}}_0$ and an equivalence of $\infty $-categories $\operatorname{\mathcal{C}}\rightarrow \operatorname{N}_{\bullet }( \operatorname{\mathcal{C}}_0 )$.