Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Example 5.3.5.4. Let $\operatorname{\mathcal{C}}$ be a $2$-category and let $\operatorname{Pith}(\operatorname{\mathcal{C}})$ denote its pith (Construction 2.3.2.10). 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.