\node[] (i1j0) at (1, -1) {P};
\node[] (i1j1) at (1, 1) {C};
\node[] (i0j0)  at (-1, -1) {B};
\node[] (i0j1)  at (-1, 1) {A};

\draw[<-] (i0j0) -- (i0j1) node [midway] {$f$};
\draw[->] (i0j0) -- (i1j0) node [midway, below] {$i_1$};
\draw[->] (i0j1) -- (i1j1) node [midway] {$g$};
\draw[<-] (i1j0) -- (i1j1) node [midway, right] {$i_2$};