$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
4.1
\begin{equation} \begin{gathered}\label{equation:lifting-problem-in-characterization} \xymatrix@R =50pt@C=50pt{ \Lambda ^{n}_{i} \ar [r]^-{\sigma _0} \ar [d] & \operatorname{N}_{\bullet }(\operatorname{\mathcal{E}}) \ar [d]^{ \operatorname{N}_{\bullet }(U) } \\ \Delta ^ n \ar [r]^-{\tau } \ar@ {-->}[ur] & \operatorname{N}_{\bullet }(\operatorname{\mathcal{C}}) } \end{gathered} \end{equation}