Auslander-Buchweitz Context and Co-t-structures

作者：Mendoza Hernandez Octavio; Saenz Valadez Edith Corina; Santiago Vargas Valente; Souto Salorio Maria Jose

来源：Applied Categorical Structures, 2013, 21(5): 417-440.

DOI：10.1007/s10485-011-9271-2

• Auslander-Buchweitz approximation theory
• Triangulated categories
• Relative homology
• Homological dimensions
• Co-t-structures in triangulated categories

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 3.8). In the Krull-Schmidt case, we establish a bijective correspondence between co-t-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 omega induces a bounded non-degenerated co-t-structure on the smallest thick triangulated subcategory of containing omega. We also give a description of the bounded co-t-structures on (see Theorem 5.10). 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 Happel and Reiten, Math Z 232:559-588, 1999), we give a bijective correspondence between finite silting generator sets omega = add (omega) and bounded co-t-structures (see Theorem 6.7).

• 出版日期2013-10