Example 4.8.1.4. Let $\operatorname{\mathcal{C}}$ be a $2$-category, and suppose that every $2$-morphism in $\operatorname{\mathcal{C}}$ is an isomorphism. Then the Duskin nerve $\operatorname{N}_{\bullet }^{\operatorname{D}}(\operatorname{\mathcal{C}})$ is a $(2,1)$-category, in the sense of Definition 4.8.1.8. This follows by combining Propositions 4.8.1.7 and 2.3.3.1.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$