$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
8.77
\begin{equation} \begin{gathered}\label{equation:compare-dagger-with-conjugacy2} \xymatrix@C =50pt@R=50pt{ \operatorname{Tw}(\operatorname{\mathcal{E}}^{\dagger }) \ar [r]^-{(\lambda _{+}, \iota \circ \operatorname{Tw}(U^{\dagger }))} \ar [d]^{ \operatorname{Tw}(U^{\dagger }) } & \operatorname{\mathcal{E}}^{\dagger } \times _{\operatorname{\mathcal{C}}^{\operatorname{op}} } \operatorname{Tw}(\operatorname{\mathcal{C}}) \ar [r]^-{T} \ar [d] & \operatorname{\mathcal{E}}\ar [d]^{ U } \\ \operatorname{Tw}( \operatorname{\mathcal{C}}^{\operatorname{op}} ) \ar [r]^-{ \iota } & \operatorname{Tw}(\operatorname{\mathcal{C}}) \ar [r] & \operatorname{\mathcal{C}}. } \end{gathered} \end{equation}