Kerodon

\begin{equation} \begin{gathered}\label{equation:compatibilities-of-Xi} \xymatrix@R =50pt@C=50pt{ \operatorname{\mathcal{C}}\ar [d]^{ \rho _{-} } & \operatorname{Fun}(\Delta ^1,\operatorname{\mathcal{C}}) \ar [l]_{\operatorname{ev}_0} \ar [r]^-{ \operatorname{ev}_{1} } \ar [d]^{\Xi } & \operatorname{\mathcal{C}}\ar [d]^{\rho _{+}} \\ \operatorname{Cospan}(\operatorname{\mathcal{C}}^{\operatorname{op}}) & \operatorname{Cospan}( \operatorname{Tw}(\operatorname{\mathcal{C}}) ) \ar [l]_{ \operatorname{Cospan}(\lambda _{-}) } \ar [r]^-{ \operatorname{Cospan}(\lambda _{+} ) } & \operatorname{Cospan}(\operatorname{\mathcal{C}}), } \end{gathered} \end{equation}