# Kerodon

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

Corollary 8.1.4.12. Let $\operatorname{\mathcal{C}}$ be a category which admits pushouts. Then the comparison map of Example 8.1.4.10 determines an isomorphism of simplicial sets

$\operatorname{Cospan}( \operatorname{N}_{\bullet }(\operatorname{\mathcal{C}}) ) \rightarrow \operatorname{N}_{\bullet }^{\operatorname{D}}( \operatorname{Cospan}(\operatorname{\mathcal{C}}) ).$