Kerodon

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

Corollary 2.3.1.10. Let $\operatorname{\mathcal{C}}$ be a $2$-category. Then the Duskin nerve $\operatorname{N}_{\bullet }^{\operatorname{D}}(\operatorname{\mathcal{C}})$ is $3$-coskeletal (Definition ). In other words, if $S_{\bullet }$ is a simplicial set, then any map from the $3$-skeleton $\operatorname{sk}_{3}( S_{\bullet } ) \rightarrow \operatorname{N}_{\bullet }^{\operatorname{D}}(\operatorname{\mathcal{C}})$ extends uniquely to a map $S_{\bullet } \rightarrow \operatorname{N}_{\bullet }^{\operatorname{D}}(\operatorname{\mathcal{C}})$.