$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
5.9
\begin{equation} \begin{gathered}\label{equation:fully-faithful-check-cartesian} \xymatrix@R =50pt@C=50pt{ \operatorname{Hom}_{\operatorname{\mathcal{C}}}(X,Y,Z) \times _{ \operatorname{Hom}_{\operatorname{\mathcal{C}}}(Y,Z) } \{ g\} \ar [r] \ar [d] & \operatorname{Hom}_{\operatorname{\mathcal{C}}}(X,Z) \ar [d] \\ \operatorname{Hom}_{\operatorname{\mathcal{D}}}( U(X), U(Y), U(Z) ) \times _{ \operatorname{Hom}_{\operatorname{\mathcal{D}}}( U(Y), U(Z)) } \{ U(g) \} \ar [r] & \operatorname{Hom}_{\operatorname{\mathcal{D}}}( U(X), U(Z) ) } \end{gathered} \end{equation}