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arXiv · 1010.0351

From triangulated categories to module categories via localisation

Aslak Bakke Buan·Bethany Marsh
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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.

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Aslak Bakke Buan, Bethany Marsh. 2010-10-02. From triangulated categories to module categories via localisation. https://doi.org/10.1090/s0002-9947-2012-05631-5

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