From triangulated categories to module categories via localisation
Representation Theory
2020-12-21 v2 Category Theory
Abstract
We show that the category of finite-dimensional modules over the endomorphism algebra of a rigid object in a Hom-finite triangulated category is equivalent to the Gabriel-Zisman localisation of the category with respect to a certain class of maps. This generalises the 2-Calabi-Yau tilting theorem of Keller-Reiten, in which the module category is obtained as a factor category, to the rigid case.
Cite
@article{arxiv.1010.0351,
title = {From triangulated categories to module categories via localisation},
author = {Aslak Bakke Buan and Bethany Marsh},
journal= {arXiv preprint arXiv:1010.0351},
year = {2020}
}
Comments
New section describing relationship to work of Nakaoka on cotorsion pairs. To appear in Transactions of the American Mathematical Society. 18 pages; no separate figures