\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{arrows.meta}

\begin{document}

\begin{tikzpicture}
\node (a) at (0,0) {$A$};
\node (b) at (1.5,0) {$B,$};
\draw[->] (a) to [bend left] node[scale=.7] (f) [above] {$1_{B} \circ f$} (b);
\draw[->] (a) to [bend right] node[scale=.7] (g) [below] {$f$} (b);
\draw[-{Implies},double distance=1.5pt,shorten >=2pt,shorten <=2pt] (f) to node[scale=.7] [right] {$\lambda_{f}$} (g);
\node (c) at (2,0) {$A$};
\node (d) at (3.5,0) {$B$};
\draw[->] (c) to [bend left] node[scale=.7] (h) [above] {$f \circ 1_{A}$} (d);
\draw[->] (c) to [bend right] node[scale=.7] (i) [below] {$f$} (d);
\draw[-{Implies},double distance=1.5pt,shorten >=2pt,shorten <=2pt] (h) to node[scale=.7] [right] {$\rho_{f}$} (i);


\end{tikzpicture}

\end{document}