$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
7.27
\begin{equation} \begin{gathered}\label{equation:relative-Kan-extension-mapping-property} \xymatrix@R =50pt@C=50pt{ \operatorname{Hom}_{ \operatorname{Fun}(\operatorname{\mathcal{C}}, \operatorname{\mathcal{D}})}( F, G ) \ar [r] \ar [d] & \operatorname{Hom}_{ \operatorname{Fun}( \operatorname{\mathcal{C}}^{0}, \operatorname{\mathcal{D}}) }( F_0, G_0) \ar [d] \\ \operatorname{Hom}_{ \operatorname{Fun}(\operatorname{\mathcal{C}}, \operatorname{\mathcal{E}}) }( U \circ F, U \circ G) \ar [r] & \operatorname{Hom}_{ \operatorname{Fun}( \operatorname{\mathcal{C}}^{0}, \operatorname{\mathcal{E}}) }( U \circ F_0, U \circ G_0). } \end{gathered} \end{equation}