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

\draw[->] (a) to[out=45,in=135] node[midway] (f) {$q \circ f$} (b);
\draw[->] (a) to[out=-45,in=-135] node[midway,below] (g) {$g \circ p$} (b);
\draw[double,->] ([yshift=-2pt]f.south) -- node[midway,right] {$\sigma$} ([yshift=2pt]g.north);