From triangulated categories to module categories via localisation
arXiv:1010.0351 · doi:10.1090/S0002-9947-2012-05631-5
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.
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
References in corpus (2)
Cited by in corpus (11)
- From triangulated categories to module categories via localisation II: Calculus of fractions
- Coloured quivers for rigid objects and partial triangulations: The unpunctured case
- The index with respect to a rigid subcategory of a triangulated category
- Quasi-abelian hearts of twin cotorsion pairs on triangulated categories
- From triangulated categories to module categories via homotopical algebra
- Localizations of the hearts of cotorsion pairs associated with mutations
- A resolution theorem for extriangulated categories with applications to the index
- Abelian categories from triangulated categories via Nakaoka-Palu's localization
- Abelian quotients of the categories of short exact sequences
- Silting reduction in extriangulated categories
- Localization of triangulated categories with respect to extension-closed subcategories