In an abelian category, a short exact sequence $0 \to A \buildrel f \over \to B \buildrel g \over \to C \to 0$ is split if it satisfies the following equivalent conditions:

(a) there exists a homomorphism $h : C \to B$ such that $gh = 1_C$

(b) there exists a homomorphism $j : B \to A$ such that $jf = 1_A$

(c) $B$ is isomorphic to the direct sum $A \oplus C$

In this case, we say that $h$ and $j$ are backmaps or splitting backmaps.