Abelian quotients of triangulated categories
Representation Theory
2015-07-21 v2
Abstract
We study abelian quotient categories A=T/J, where T is a triangulated category and J is an ideal of T. Under the assumption that the quotient functor is cohomological we show that it is representable and give an explicit description of the functor. We give technical criteria for when a representable functor is a quotient functor, and a criterion for when J gives rise to a cluster-tilting subcategory of T. We show that the quotient functor preserves the AR-structure. As an application we show that if T is a finite 2-Calabi-Yau category, then with very few exceptions J is a cluster-tilting subcategory of T.
Keywords
Cite
@article{arxiv.1501.03021,
title = {Abelian quotients of triangulated categories},
author = {Benedikte Grimeland and Karin Marie Jacobsen},
journal= {arXiv preprint arXiv:1501.03021},
year = {2015}
}
Comments
20 pages. Minor changes; have stated more explicitly where finiteness is required