Auslander-Buchweitz Context and Co-t-structures

We show that the relative Auslander-Buchweitz context on a triangulated category T coincides with the notion of co-t-structure on certain triangulated subcategory of T (see Theorem 3.8). In the Krull-Schmidt case, we stablish a bijective correspondence between cot-structures and cosuspended, precovering subcategories (see Theorem 3.11). 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 T containing ω. We also give a description of the bounded co-t-structures on T (see Theorem 5.10). Finally, as an application to the particular case of the bounded derived category Db(H), where H is an abelian hereditary category which is Hom-finite, Ext-finite and has a tilting object (see [10]), we give a bijective correspondence between finite silting generator sets ω = add (ω) and bounded co-t-structures (see Theorem 6.7).