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A triangulated category is an additive category equipped with the additional structure of an autoequivalence (called the translation functor) and a class of of triangles satisfying certain axioms.

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Equivalences between $D^b(\mathcal{B})$ and $\mathcal{D}_{\mathcal{B}}$, the triangulated ca...

In the paper "Finite dimensional algebras and highest weight categories" of Cline, Parshall and Scott is stated as follows: Let $\mathcal{B}$ be an abelian subcategory of a triangulated category $ …