Kerodon

\begin{equation} \begin{gathered}\label{equation:big-diagram-dual-fibration} \xymatrix@C =50pt@R=100pt{ \{ \textnormal{Cocartesian fibrations $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$} \} \ar@ {<=>}[r]^{ U \longleftrightarrow U^{\operatorname{op}} } \ar@ {<=>}[dr]^{ U \longleftrightarrow U^{\vee } } \ar@ {<=>}[d]^{U \longleftrightarrow U^{\dagger }} & \{ \textnormal{Cartesian fibrations $U': \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}^{\operatorname{op}}$} \} \ar@ {<=>}[d]^{ V^{\dagger } \longleftrightarrow V} \\ \{ \textnormal{Cartesian fibrations $V': \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}^{\operatorname{op}}$} \} \ar@ {<=>}[r]^{V^{\operatorname{op}} \longleftrightarrow V} & \{ \textnormal{Cocartesian fibrations $V: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$} \} } \end{gathered} \end{equation}