Definition 37.2:

A short exact sequence of abelian groups/chain complexes

$$\begin{CD} 0@> >> L @> f >> G @> g >> K @> >> 0, \end{CD} \eqno(37.6)$$

splits on the right if there exists a group homomorphism (respectively a chain map) $\phi:K\longrightarrow G$ such that $g \circ \phi =$   id$_K$. The short exact sequence (37.6) splits on the left if there exists group homomorphism (respectively a chain map) $\theta:G\longrightarrow L$ such that $\theta \circ f =$   id$_L$.