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

\draw[<-] (i0j0) -- (i0j1) node [midway] {$f$};
\draw[->] (i0j1) -- (i1j1) node [midway] {$g$};