Kerodon

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7.15
\begin{equation} \begin{gathered}\label{equation:diagram-of-Res} \xymatrix@R =50pt@C=50pt{ \operatorname{Res}_{\overline{\operatorname{\mathcal{K}}} / \operatorname{\mathcal{C}}}(\operatorname{\mathcal{D}}\times \overline{\operatorname{\mathcal{K}}}) \ar [rr] \ar [dd]^{U \circ } \ar [dr]^{T} & & \operatorname{Res}_{\operatorname{\mathcal{K}}/\operatorname{\mathcal{C}}}( \operatorname{\mathcal{D}}\times \operatorname{\mathcal{K}}) \ar [dd]^{U \circ } \ar [dl] \\ & \operatorname{\mathcal{C}}& \\ \operatorname{Res}_{ \overline{\operatorname{\mathcal{K}}}/\operatorname{\mathcal{C}}}( \operatorname{\mathcal{E}}\times \overline{\operatorname{\mathcal{K}}}) \ar [rr] \ar [ur] & & \operatorname{Res}_{ \operatorname{\mathcal{K}}/ \operatorname{\mathcal{C}}}( \operatorname{\mathcal{E}}\times \operatorname{\mathcal{K}}), \ar [ul] } \end{gathered} \end{equation}