Kerodon

Example 4.4.3.4. Let $\operatorname{\mathcal{C}}$ be a $(2,1)$-category, so that the Duskin nerve $\operatorname{N}_{\bullet }^{\operatorname{D}}(\operatorname{\mathcal{C}})$ is an $\infty $-category (Theorem 2.3.2.1). Then the core $\operatorname{N}_{\bullet }^{\operatorname{D}}(\operatorname{\mathcal{C}})^{\simeq }$ can be identified with the Duskin nerve of the $2$-groupoid $\operatorname{\mathcal{C}}^{\simeq }$ (Construction 2.2.8.27). That is, we have a canonical isomorphism $\operatorname{N}_{\bullet }^{\operatorname{D}}(\operatorname{\mathcal{C}})^{\simeq } \simeq \operatorname{N}_{\bullet }^{\operatorname{D}}(\operatorname{\mathcal{C}}^{\simeq })$.