Example 9.3.2.11. Let $\operatorname{\mathcal{QC}}$ be the $\infty $-category of (small) $\infty $-categories (Construction 5.5.4.1). Then an object $\operatorname{\mathcal{C}}\in \operatorname{\mathcal{QC}}$ is discrete (in the sense of Definition 9.3.2.1) if and only if it satisfies the following pair of conditions:
The $\infty $-category $\operatorname{\mathcal{C}}$ is locally discrete: that is, there exists an equivalence $\operatorname{\mathcal{C}}\rightarrow \operatorname{N}_{\bullet }(\operatorname{\mathcal{C}}_0)$, where $\operatorname{\mathcal{C}}_0$ is an ordinary category (Remark 9.3.2.10).
For every object $X \in \operatorname{\mathcal{C}}_0$, the automorphism group $\operatorname{Aut}(X)$ is trivial.
See Proposition 9.3.1.23. Beware that the second condition cannot be omitted.