Kerodon

Example 5.4.5.4. Let $\operatorname{\mathcal{C}}$ be a $2$-category and let $\operatorname{Pith}(\operatorname{\mathcal{C}})$ denote its pith (Construction 2.2.8.9). Then the inclusion $\operatorname{Pith}(\operatorname{\mathcal{C}}) \hookrightarrow \operatorname{\mathcal{C}}$ induces an isomorphism of simplicial sets $\operatorname{N}_{\bullet }^{\operatorname{D}}( \operatorname{Pith}(\operatorname{\mathcal{C}}) ) \simeq \operatorname{Pith}( \operatorname{N}_{\bullet }^{\operatorname{D}}(\operatorname{\mathcal{C}}) )$. This is an immediate consequence of Theorem 2.3.2.5.