Consider
\begin{document}
\usepackage{tikz-cd}
\begin{tikzcd}
T \arrow[r, "\eta T"] \arrow[swap, d, "T \eta" red ]
& T^2 \arrow[d, "\mu" red] \\
T^2 \arrow[swap, r, red, "\mu" blue]
& T
\end{tikzcd}
\end{document}
How can I draw a diagonal arrow from the top left node to the bottom right node? In addition, how can I draw an arrow parallel to this arrow? I looked in the documentation for the package but could not find the answer.
\arrow[dr, shift left]\arrow[dr, shift right]
. Which documentation did you search in? This appears on page 2. Parallel arrows appear on page 9