Corollary 8.1.3.15. Let $\operatorname{\mathcal{C}}$ be a category which admits pushouts. Then the comparison map of Example 8.1.3.13 determines an isomorphism of simplicial sets
\[ \operatorname{Cospan}( \operatorname{N}_{\bullet }(\operatorname{\mathcal{C}}) ) \rightarrow \operatorname{N}_{\bullet }^{\operatorname{D}}( \operatorname{Cospan}(\operatorname{\mathcal{C}}) ). \]