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\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);