\documentclass{article}
\usepackage{gastex}

\begin{document}

% Diagram

\begin{center}
\begin{picture}(105,28)(-33,-3)
\put(-33,-3){\framebox(105,28){}}
  \gasset{Nframe=n,Nadjust=w,Nh=6,Nmr=0}
  \node(L)(0,20){$\mathcal{L}$}
  \node(F)(30,20){$[F^V\to F]$}
  \node(O1)( 20,0){$(\mathcal{P}(R)^V\to 2^{M\times\mathcal{P}(R)})$}
  \node(O2)(-20,0){$(\mathcal{P}(R)^V\to 2^M)$}
  \node(B1)( 60,0){$(\mathcal{P}(R)^V\to F)$}

  \drawedge[ELpos=40](L,F){$[\![ -]\!]$}
  \drawedge(L,O1){$X_F$}
  \drawedge(F,O1){$\chi$}
  \drawedge[ELside=r](L,O2){$X_M$}
  \drawedge[ELpos=55](O1,B1){$\sqcup$}
  \drawedge[ELside=r,ELpos=53](O1,O2){$\mathrm{Re}$}
\end{picture}
\end{center}

\end{document}