Definition 5

A morphism of complexes $f : C \to C'$ is called a homotopism if there exists a morphism $f' : C' \to C$ such that $f' \circ f$ and $f \circ f'$ are homotopic to $1_C$ and $1_{C'}$ respectively.

It is clear that $f'$ is then also a homotopism; one also says that $f'$ is reciprocal of $f$ up to homotopy. If $f'$ and $f'_1$ are both reciprocals of $f$ up to homotopy, then $f'$ and $f'_1$ are homotopic (indeed by the preceding corollary, $f'_1 = f'_1 \circ 1_{C'}$ is homotopic to $f'_1 \circ f \circ f'$, hence to $1_C \circ f' = f'$).