\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}