Kerodon

Remark 8.1.6.2 (Symmetry). Let $\operatorname{\mathcal{C}}$ be a simplicial set and let $L$ and $R$ be collections of edges of $\operatorname{\mathcal{C}}$. Then the isomorphism $\operatorname{Cospan}(\operatorname{\mathcal{C}}) \xrightarrow {\sim } \operatorname{Cospan}( \operatorname{\mathcal{C}})^{\operatorname{op}}$ of Remark 8.1.3.4 restricts to an isomorphism of simplicial subsets $\operatorname{Cospan}^{L,R}(\operatorname{\mathcal{C}}) \xrightarrow {\sim } \operatorname{Cospan}^{R,L}(\operatorname{\mathcal{C}})^{\operatorname{op}}$.