\node (sq1_b00) at (-3, 1)  {$F(c\prime)$};
\node (sq1_a10) at (-1, 1)  {$F(c)$};
\node (sq1_b01) at (-3, -1) {$G(c\prime)$};
\node (sq1_b11) at (-1, -1) {$G(c)$};

\draw[->] (sq1_b00) -- node[midway]        {$F(f)$} (sq1_a10);
\draw[->] (sq1_a10) -> node[midway]        {$\alpha_{c}$} (sq1_b11);
\draw[->] (sq1_b00) -> node[midway,left]   {$\alpha_{c\prime}$} (sq1_b01);
\draw[->] (sq1_b01) -> node[midway,below]  {$G(f)$} (sq1_b11);