From triangulated categories to module categories via localisation

Details From triangulated categories to module categories via localisation From triangulated categories to module categories via localisation

2010-10-02

arxiv.org/abs/1010.0351v2

Mathematics

Representation Theory

New section describing relationship to work of Nakaoka on cotorsion pairs. To appear in Transactions of the American Mathemati

Scientific paper

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.

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