$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
6.12
\begin{equation} \begin{gathered}\label{equation:localization-and-categorical-pushout-easy2} \xymatrix@C =50pt@R=50pt{ \operatorname{Fun}( \operatorname{\mathcal{D}}, \operatorname{\mathcal{E}}) \ar [r]^{\circ F} \ar [d] & \operatorname{Fun}( \operatorname{\mathcal{C}}[W^{-1}], \operatorname{\mathcal{D}}) \ar [r] \ar [d] & \operatorname{Fun}(\operatorname{\mathcal{C}}, \operatorname{\mathcal{E}}) \ar [d]^{ \circ T} \\ \operatorname{Fun}( \operatorname{\mathcal{D}}_0, \operatorname{\mathcal{E}}) \ar [r]^{ \circ F_0} & \operatorname{Fun}( \operatorname{\mathcal{D}}_0[W_0^{-1}], \operatorname{\mathcal{E}}) \ar [r] & \operatorname{Fun}( \operatorname{\mathcal{D}}_0, \operatorname{\mathcal{E}}). } \end{gathered} \end{equation}