12.3.3 Pentagon Diagram
Define
\newlength{\ThreeCm}
\setlength{\ThreeCm}{3.0cm}
The code
\begin{tikzcd}[row sep={0*\the\DL,between origins}, column sep={0*\the\DL,between origins}, background color=backgroundColor, ampersand replacement=\&]
\&[0.30901699437\ThreeCm]
\&[0.5\ThreeCm]
A\otimes_{R}(A\otimes_{R}A)
\&[0.5\ThreeCm]
\&[0.30901699437\ThreeCm]
\\[0.58778525229\ThreeCm]
\webleft(A\otimes_{R}A\webright)\otimes_{R}A
\&[0.30901699437\ThreeCm]
\&[0.5\ThreeCm]
\&[0.5\ThreeCm]
\&[0.30901699437\ThreeCm]
A\otimes_{R}A
\\[0.95105651629\ThreeCm]
\&[0.30901699437\ThreeCm]
A\otimes_{R}A
\&[0.5\ThreeCm]
\&[0.5\ThreeCm]
A
\&[0.30901699437\ThreeCm]
% 1-Arrows
% Left Boundary
\arrow[from=2-1,to=1-3,"\alpha^{\Mod_{R}}_{A,A,A}"{pos=0.4125}]%
\arrow[from=1-3,to=2-5,"\id_{A}\otimes_{R}\mu^{\times}_{A}"{pos=0.6}]%
\arrow[from=2-5,to=3-4,"\mu^{\times}_{A}"{pos=0.425}]%
% Right Boundary
\arrow[from=2-1,to=3-2,"\mu^{\times}_{A}\otimes_{R}\id_{A}"'{pos=0.425}]%
\arrow[from=3-2,to=3-4,"\mu^{\times}_{A}"']%
\end{tikzcd}
will produce the following pentagon diagram:
To make the diagram larger, one could use e.g.
\newlength{\FourCm}
\setlength{\FourCm}{2.0cm}
and replace all instances of \ThreeCm with \FourCm in the code above.