Kerodon

\begin{equation} \begin{gathered}\label{equation::relative-Kan-extension-existence-transitivity2} \xymatrix@R =50pt@C=50pt{ \operatorname{\mathcal{C}}^{0} \ar [d] \ar [r]^-{F|_{\operatorname{\mathcal{C}}^{0}}} & \operatorname{\mathcal{D}}\ar [d]^{U} \\ \overline{\operatorname{\mathcal{C}}} \ar [r] \ar@ {-->}[ur]^{ \overline{F} } & \operatorname{\mathcal{E}}, } \end{gathered} \end{equation}