Kerodon

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7.21
\begin{equation} \begin{gathered}\label{equation:relative-Kan-extension-existence2} \xymatrix@R =50pt@C=50pt{ \operatorname{\mathcal{K}}\ar [rr]^{ F_0 \circ \pi } \ar [d] & & \operatorname{\mathcal{D}}\ar [d]^{U} \\ \operatorname{\mathcal{K}}\star _{\operatorname{\mathcal{C}}} \operatorname{\mathcal{C}}\ar [r]^-{S} \ar [urr]^{ \overline{F} } & \operatorname{\mathcal{C}}\ar [r]^-{G} & \operatorname{\mathcal{E}}. } \end{gathered} \end{equation}