\node (gamma) at (0, 2) {$\Gamma$};

\node (prod) at (0, 0) {$\beta^\alpha \times \alpha$};

\node (arg) at (2.5, 0) {$\alpha$};
\node (func) at (-2.5, 0) {$\beta^\alpha$};

\draw[->] (gamma) -- node[midway] {$\left<f,x\right>$} (prod);
\draw[->] (prod) -- node[midway] {$\pi_1$} (func);
\draw[->] (prod) -- node[midway,below] {$\pi_2$} (arg);
\draw[->] (gamma) -- node[midway] {$f$} (func);
\draw[->] (gamma) -- node[midway] {$x$} (arg);