Auslander–Buchweitz Context and CoEmphasis Type=

Authors: Octavio Mendoza Hernández Edith Corina Sáenz Valadez Valente Santiago Vargas María José Souto Salorio

Publish Date: 2011/10/28

Volume: 21, Issue: 5, Pages: 417-440

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Abstract

We show that the relative Auslander–Buchweitz context on a triangulated category mathcalT coincides with the notion of cotstructure on certain triangulated subcategory of mathcalT see Theorem 38 In the Krull–Schmidt case we establish a bijective correspondence between cotstructures and cosuspended precovering subcategories see Theorem 311 We also give a characterization of bounded cotstructures in terms of relative homological algebra The relationship between silting classes and cotstructures is also studied We prove that a silting class ω induces a bounded nondegenerated cotstructure on the smallest thick triangulated subcategory of mathcalT containing ω We also give a description of the bounded cotstructures on mathcalT see Theorem 510 Finally as an application to the particular case of the bounded derived category mathbfDbmathcalH where mathcalH is an abelian hereditary category which is Homfinite Extfinite and has a tilting object see Happel and Reiten Math Z 232559–588 1999 we give a bijective correspondence between finite silting generator sets ω = add ω and bounded cotstructures see Theorem 67

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