\node (atop) at (-1, 0.5) {a};
\node (abot) at (-1, -0.5) {a};
\node (btop) at (1, 0.5) {b};
\node (bbot) at (1, -0.5) {b};

\draw[->] (atop) to[out=30,in=150] node[midway] (f) {f} (btop);
\draw[->] (atop) -- (abot);
\draw[->] (abot) to[out=-30,in=-150] node[midway,below] (g) {g} (bbot);
\draw[->] (btop) -- (bbot);

\node at (0, 0) {$\alpha$};