Auslander-Buchweitz context and co-t-structures
Abstract
We show that the relative Auslander-Buchweitz context on a triangulated category coincides with the notion of co-t-structure on certain triangulated subcategory of (see Theorem M2). In the Krull-Schmidt case, we stablish a bijective correspondence between co-t-structures and cosuspended, precovering subcategories (see Theorem correspond). We also give a characterization of bounded co-t-structures in terms of relative homological algebra. The relationship between silting classes and co-t-structures is also studied. We prove that a silting class ω induces a bounded non-degenerated co-t-structure on the smallest thick triangulated subcategory of containing ω. We also give a description of the bounded co-t-structures on (see Theorem Msc). Finally, as an application to the particular case of the bounded derived category (), where is an abelian hereditary category which is Hom-finite, Ext-finite and has a tilting object (see HR), we give a bijective correspondence between finite silting generator sets ω=\,(ω) and bounded co-t-structures (see Theorem teoH).