$$
\def\M{{\cal M}\dot} \def\inv{^{-1}} \def\orlz#1{\langle#1\rangle}
\let\labelstyle\textstyle
\Dg
[q(g,b),t] \aNul (1,-1) \aMapsto (2,-4) &&& \rMapsto &&&
                 q(g,\phi(b,t)) \aNul (-1,-1) \aMapsto (-2,-4) \mx{12pt} \\
       & \M R_s &       & \rTo    &        & \beta\inv(W_s)   \\
       &        & \rdTo &         & \ldTo >{R_s}              \\
       &        &       & \beta\inv\orlz{s}                   \\
       &  & q(g,r_s(b)) & {} = {} & q(g,r_s(\phi(b,t)))                  \\
\endDg
$$