$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
7.36
\begin{equation} \begin{gathered}\label{equation:coslice-over-Kan-extension2} \xymatrix@R =50pt@C=50pt{ \operatorname{Hom}_{ \operatorname{Fun}(\operatorname{\mathcal{C}}, \operatorname{\mathcal{D}})}( F, \underline{D} ) \ar [r] \ar [d] & \operatorname{Hom}_{ \operatorname{Fun}(\operatorname{\mathcal{C}}^{0}, \operatorname{\mathcal{E}}) }( F_0, \underline{D}|_{ \operatorname{\mathcal{C}}^{0} } ) \ar [d] \\ \operatorname{Hom}_{ \operatorname{Fun}(\operatorname{\mathcal{C}}, \operatorname{\mathcal{E}})}( U \circ F, U \circ \underline{D} ) \ar [r] & \operatorname{Hom}_{ \operatorname{Fun}(\operatorname{\mathcal{C}}^{0}, \operatorname{\mathcal{E}})}( U \circ F_0, U \circ \underline{D}|_{ \operatorname{\mathcal{C}}^{0} } ). } \end{gathered} \end{equation}