Additive functors preserve quasi-isomorphisms between projective complexes

Corollary 6.6.12. Let \(F\colon \Ch (\Aa ) \to \Ch (\Bb )\) be a functor that preserves chain homotopies (for example, a functor induced by an additive functor \(\Aa \to \Bb \)). Then \(F\) preserves quasi-isomorphisms between bounded below projective chain complexes. □