## 13.1 Introduction

We first discuss triangulated categories and localization in triangulated categories. Next, we prove that the homotopy category of complexes in an additive category is a triangulated category. Once this is done we define the derived category of an abelian category as the localization of the homotopy category with respect to quasi-isomorphisms. A good reference is Verdier's thesis [Verdier].

Comment #3654 by Tim Holzschuh on

'[...] as the localization of the of homotopy category with respect to quasi-isomorphisms.' I guess the second 'of' isn't supposed to be there.

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