$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
7.52
\begin{equation} \begin{gathered}\label{equation:left-fibration-Kan-extension-characterization} \xymatrix { \operatorname{\mathcal{E}}^{0}_{/X} \ar [r] \ar [d] & \operatorname{\mathcal{E}}_{/X} \ar [d] \\ \operatorname{\mathcal{E}}\times _{ \operatorname{\mathcal{C}}} \operatorname{\mathcal{C}}^{0}_{/C} \ar [r]^{\iota _{C}} & \operatorname{\mathcal{E}}\times _{\operatorname{\mathcal{C}}} \operatorname{\mathcal{C}}_{/C}. } \end{gathered} \end{equation}