$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
7.4
\begin{equation} \begin{gathered}\label{equation:relative-colimit-by-fiber-preliminary} \xymatrix@R =50pt@C=50pt{ \operatorname{Hom}_{\operatorname{Fun}(K^{\triangleright }, \operatorname{\mathcal{E}}) }( \overline{q}, \underline{X}) \ar [r] \ar [d] & \operatorname{Hom}_{\operatorname{Fun}(K, \operatorname{\mathcal{E}}) }( q, \underline{X}|_{K} ) \ar [d] \\ \operatorname{Hom}_{\operatorname{Fun}(K^{\triangleright }, \operatorname{\mathcal{C}}) }( U \circ \overline{q}, U \circ \underline{X}) \ar [r] & \operatorname{Hom}_{\operatorname{Fun}(K, \operatorname{\mathcal{C}}) }( U \circ q, U \circ \underline{X}|_{K}) } \end{gathered} \end{equation}