Kerodon

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8.31
\begin{equation} \begin{gathered}\label{equation:collapse-left-universal} \xymatrix@R =50pt@C=50pt{ \operatorname{Fun}_{\pm }( \operatorname{\mathcal{C}}, \operatorname{\mathcal{D}}) \ar [r] \ar [d] & \operatorname{Fun}( \operatorname{\mathcal{C}}_{-}, \operatorname{\mathcal{D}}_{-} )^{\operatorname{op}} \ar [d]^{\circ \lambda _{-}} \\ \operatorname{\mathcal{E}}_{-} \times _{ \operatorname{Fun}( \operatorname{\mathcal{C}}, \operatorname{\mathcal{D}}_{+} ) } \operatorname{Fun}(\operatorname{\mathcal{C}}_{+}, \operatorname{\mathcal{D}}_{+} ) \ar [r] \ar [d] & \operatorname{Fun}( \operatorname{\mathcal{C}}[W^{-1}], \operatorname{\mathcal{D}}^{\operatorname{op}}_{-} ) \ar [d] \\ \operatorname{Fun}( \operatorname{\mathcal{C}}, \operatorname{\mathcal{D}}) \times _{ \operatorname{Fun}( \operatorname{\mathcal{C}}, \operatorname{\mathcal{D}}_{+}) } \operatorname{Fun}( \operatorname{\mathcal{C}}_{+}, \operatorname{\mathcal{D}}_{+} ) \ar [r]^-{\theta } & \operatorname{Fun}( \operatorname{\mathcal{C}}, \operatorname{\mathcal{D}}^{\operatorname{op}}_{-} ) } \end{gathered} \end{equation}