\documentclass{ppex}

\documentclass{ppex}
\nonstopmode
\usepackage [all,2cell]{xy}
\pagestyle{empty}
\setlength\textwidth{183.0pt}
\begin{document}
\ResetPreambleCommands
\ReadyForTheFray
\usepackage [all,2cell]{xy}
\UseAllTwocells
\[
\xymatrix @=15mm {
L_1 \rlowertwocell<-3>_{a_1}{<-1>}
\rcompositemap<6>_{a_2}^{a_3}{\omit}
& R_1 \dtwocell<0>_{a_4}{"}
\\ L_2 \uuppertwocell_u^d{\omit}
\rtwocell<2>{'id}
& R_2
}\]
\end{document}