\node (a) at (-1, 0) {a};
\node (b) at (1, 0) {b};

\draw[->] (a) to[out=30,in=150] node[midway] (f) {f} (b);
\draw[->] (a) to[out=-30,in=-150] node[midway,below] (g) {g} (b);
\draw[double,->] ([yshift=-2pt]f.south) -- node[midway,right] {$\alpha$} ([yshift=2pt]g.north);