\documentclass{standalone}
\usepackage{tikz} 
\usepackage{tikz-cd} 
\usepackage{amsmath}
\usetikzlibrary{arrows} 
\begin{document} 
\begin{tikzcd}[row sep=huge, column sep=huge] 
 % drawing 0- and 1-celss 
 A \arrow[dr, "f"'] 
 \arrow[rr, "\mathrm{id}_A", ""{name=id_A, below}] &&  |[alias=A]| A \arrow[dr, "f"] 
\\ 
 & |[alias=B]| B \arrow[ur,"g"] \arrow[rr, "\mathrm{id}_B"', ""{name=id_B}]  && B
 % % drawing 2-cells
 \arrow[Rightarrow, from=B, to=id_A, "\mathcal{E}"',shorten >=1em,shorten <=1em] 
 \arrow[Rightarrow, from=id_B, to=A, "\eta"',shorten >=1em,shorten <=1em] 
\end{tikzcd}
=
\begin{tikzcd}
A\arrow[r,bend left=50,""{name=F, below}]\arrow[r,bend right=50,"" name=G]\arrow[Rightarrow,from=G,to=F,"\mathrm{id}_f"'] & B
\end{tikzcd}
\end{document}