nLab Verdier's abelianization functor

Given a triangulated category $T$ there is an abelian category $A$ and an additive functor $T\to A$ satisfying certain universal property; this functor is due to Verdier and is called the Verdier’s abelianization functor. A readable and comprehensive introduction is in the monograph

• A. Neeman, Triangulated categories, Annals of Mathematics Studies 148, Princeton University Press 2001, viii+449 pp.