Homotopy category of chain complexes

Summary

Let $\mathcal{A}$ be an additive category. The homotopy category of chain complexes $K(\mathcal{A})$ has the chain complexes as objects and the chain maps modulo chain homotopy as morphisms. In it, chain homotopy equivalences become isomorphisms. It is a triangulated category, and the derived category of an abelian category is obtained from it by inverting the quasi-isomorphisms.