arXiv 1102.45972011-02math.CTmath.RT

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

Aslak Bakke Buan, Bethany Marsh

备注：: 21 pages; no separate figures. Minor changes. To appear in Journal of the London Mathematical Society (published version is different)
发表信息：: J. London Math. Soc. (2012) 86 (1): 152-170
DOI：: 10.1112/jlms/jdr077

英文摘要：

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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