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Definition

Let $A$ be an additive category. Recall the notion of chain complex, of morphisms of chain complexes in $A$, and of chain homotopy?.

We have

• $C(A)$, the category of chain complexes and chain chomplex homomorphisms in $C$;

• $K(A)$, the category obtained from $C(A)$ by identifying homotopic chain homomorphisms.

If $A$ is moreover abelian, then we also have

• $D(A)$, the derived category obtained from $C(A)$ (or $K(A)$) by inverting all quasi-isomorphisms.

Related concepts

• derived category