split short exact sequence

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 $jf=1_{A}$ ;

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