From triangulated categories to module categories via localisation
Open Access
- 7 November 2012
- journal article
- Published by American Mathematical Society (AMS) in Transactions of the American Mathematical Society
- Vol. 365 (6) , 2845-2861
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 2 -Calabi-Yau tilting theorem of Keller-Reiten, in which the module category is obtained as a factor category, to the rigid case.Keywords
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