Example 4.8.2.2. Let $n$ be an integer. Then every $(n,1)$-category is locally $(n-1)$-truncated (Corollary 4.8.1.20). In particular:
If $Q$ is a partially ordered set, then the nerve $\operatorname{N}_{\bullet }(Q)$ is locally $(-1)$-truncated $\infty $-category (Proposition 4.8.1.15).
If $\operatorname{\mathcal{C}}$ is an ordinary category, then the nerve $\operatorname{N}_{\bullet }(\operatorname{\mathcal{C}})$ is a locally $0$-truncated $\infty $-category (Example 4.8.1.3).
If $\operatorname{\mathcal{C}}$ is a $2$-category in which every $2$-morphism is an isomorphism, then the Duskin nerve $\operatorname{N}_{\bullet }^{\operatorname{D}}(\operatorname{\mathcal{C}})$ is a locally $1$-truncated $\infty $-category (Example 4.8.1.4).