Kerodon

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5.62
\begin{equation} \begin{gathered}\label{equation:universality-formulation} \xymatrix@R =50pt@C=50pt{ \operatorname{Hom}_{\operatorname{\mathcal{QC}}}( \operatorname{\mathcal{D}}_0, \operatorname{\mathcal{D}}_1) \times _{ \operatorname{Fun}( \operatorname{\mathcal{E}}, \operatorname{\mathcal{QC}})^{\simeq } } \operatorname{Fun}( \operatorname{\mathcal{E}}, \operatorname{\mathcal{QC}}_{\operatorname{Obj}} )^{\simeq } \ar [d] \ar [r] & \operatorname{Hom}_{\operatorname{\mathcal{QC}}}( \operatorname{\mathcal{D}}_0, \operatorname{\mathcal{D}}_1) \ar [d] \\ \operatorname{Fun}( \operatorname{\mathcal{E}}, \operatorname{\mathcal{QC}}_{\operatorname{Obj}} )^{\simeq } \ar [d]^{\circ h^{+}} \ar [r]^-{ V \circ } & \operatorname{Fun}( \operatorname{\mathcal{E}}, \operatorname{\mathcal{QC}})^{\simeq } \ar [d]^-{ \circ h^{+}} \\ \operatorname{Fun}( \operatorname{\mathcal{M}}, \operatorname{\mathcal{QC}}_{\operatorname{Obj}} )^{\simeq } \ar [r]^-{ V \circ } & \operatorname{Fun}( \operatorname{\mathcal{M}}, \operatorname{\mathcal{QC}})^{\simeq }, } \end{gathered} \end{equation}