Exercise 2, § 2

Let $C$ and $C’$ be two complexes of $A$-modules; suppose that the complexes $C$ and $B(C)$ (resp. $C’$ and $Z(C’)$) are projective (resp. injective). Now prove that every morphism of complexes from $H(C)$ to $H(C’)$ is induced by a morphism from $C$ to $C’$.