\documentclass{standalone}
\usepackage{tikz-cd}

\begin{document}

\begin{tikzcd}[row sep=2.5em]
T^4 
  \arrow[rr,"T^{2}\mu",""{name=C}] 
  \arrow[dr,"T \mu T",""{name=E}] 
  \arrow[dd,swap,"\mu T^2"] &&
  T^3 \arrow[dr,"T \mu"] \\
& T^3 
  \arrow[rr,"T \mu", swap, ""{name=A}] &&
  T^2 \arrow[dd,"\mu"] \\
T^3  \arrow[dr,swap,"\mu T",""{name=D}] &&  \\
& T^2 \arrow[rr,"\mu",swap,""{name=B}] \arrow[uu,<-,swap,"\mu T"] && T
\arrow[Rightarrow, from=A, to=B, "{\tau}", shorten >=1em, shorten <=1em]
\arrow[Rightarrow, from=C, to=A, "{T \tau}", shorten >=1em, shorten <=1em]
\arrow[Rightarrow, from=E, to=D, "{\tau T}", shorten >=1em, shorten <=1em]
\end{tikzcd}
=
\begin{tikzcd}[row sep=2.5em]
T^4 \arrow[rr,"T^{2}\mu",""{name=A}] \arrow[dd,swap,"\mu T^2"] &&
  T^3 \arrow[dd,swap,"\mu T"] \arrow[dr,"T \mu",""{name=D}] \\
&&&
  T^2 \arrow[dd,"\mu"] \\
T^3 \arrow[rr,"T \mu",""{name=B}] \arrow[dr,swap,"\mu T"] && T^2 \arrow[dr,swap,"\mu",""{name=E}] \\
& T^2 \arrow[rr,"\mu",swap,""{name=C}]&& T
\arrow[Rightarrow, from=A, to=B, "{\mu_{\mu}}", shorten >=1em, shorten <=1em]
\arrow[Rightarrow, from=B, to=C, "{\tau}", shorten >=1em, shorten <=1em]
\arrow[Rightarrow, from=D, to=E, "{\tau}", shorten >=1em, shorten <=1em]
\end{tikzcd}
\end{document}