\begin{tikzcd}[row sep={4.0*\the\DL,between origins}, column sep={4.0*\the\DL,between origins}, background color=backgroundColor, ampersand replacement=\&]
1
\&
\&
2
\&
\\
\&
1'
\&
\&
2'
\\
3
\&
\&
4
\&
\\
\&
3'
\&
\&
4'
% 1-Arrows
% First Square
\arrow[from=1-1,to=3-1,"f"']%
\arrow[from=3-1,to=3-3,"h"{description,pos=0.25}]%
\arrow[from=1-1,to=1-3,"g"]%
\arrow[from=1-3,to=3-3,"k"{description,pos=0.25}]%
% Second Square
\arrow[from=2-2,to=4-2,"f'"{description,pos=0.3},crossing over]%
\arrow[from=4-2,to=4-4,"h'"']%
\arrow[from=2-2,to=2-4,"g'"{description,pos=0.3},crossing over]%
\arrow[from=2-4,to=4-4,"k'"]%
% Connecting Arrows
\arrow[from=1-1,to=2-2,"c_{1}"description]%
\arrow[from=1-3,to=2-4,"c_{2}"]%
\arrow[from=3-1,to=4-2,"c_{3}"']%
\arrow[from=3-3,to=4-4,"c_{4}"description]%
\end{tikzcd}