From triangulated categories to module categories via localisation II: Calculus of fractions

Abstract

We show that the quotient of a Hom-finite triangulated category C by the kernel of the functor Hom(T, -), where T is a rigid object, is preabelian. We further show that the class of regular morphisms in the quotient admit a calculus of left and right fractions. It follows that the Gabriel-Zisman localisation of the quotient at the class of regular morphisms is abelian. We show that it is equivalent to the category of finite dimensional modules over the endomorphism algebra of T in C.

21 pages; no separate figures. Minor changes. To appear in Journal of the London Mathematical Society (published version is different)

References in corpus (1)

• From triangulated categories to module categories via localisation

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