$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
3.82
\begin{equation} \label{equation:unit-of-realization-3} \begin{gathered} \xymatrix@R =50pt@C=50pt{ & \operatorname{Sing}_{\bullet }( V \setminus \{ v\} ) \ar [r] \ar [d] & \operatorname{Sing}_{\bullet }( V ) \ar [d] \\ \operatorname{Sing}_{\bullet }(|\operatorname{\partial \Delta }^{n}|) \ar [r] \ar [d] & \operatorname{Sing}_{\bullet }( | \Delta ^{n} | \setminus \{ v \} ) \ar [r] \ar [d] & \operatorname{Sing}_{\bullet }(|\Delta ^ n|) \ar [d] \\ \operatorname{Sing}_{\bullet }(|X'|) \ar [r] & \operatorname{Sing}_{\bullet }( |X| \setminus \{ x\} ) \ar [r] & \operatorname{Sing}_{\bullet }(|X|). }\end{gathered} \end{equation}