From triangulated categories to module categories via localisation II: Calculus of fractions
Category Theory
2020-12-21 v2 Representation Theory
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.
Keywords
Cite
@article{arxiv.1102.4597,
title = {From triangulated categories to module categories via localisation II: Calculus of fractions},
author = {Aslak Bakke Buan and Bethany Marsh},
journal= {arXiv preprint arXiv:1102.4597},
year = {2020}
}
Comments
21 pages; no separate figures. Minor changes. To appear in Journal of the London Mathematical Society (published version is different)