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

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

2011-02-22

arxiv.org/abs/1102.4597v2

Mathematics

Category Theory

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

Scientific paper

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.

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