Cut cotorsion pairs. (10th September 2022)

• Record Type: Journal Article
• Authors: Huerta, Mindy; Mendoza, Octavio; Pérez, Marco A.
• Is Part Of: Glasgow mathematical journal. Volume 64:Part 3(2022)
• Page Start: 548
• Page End: 585
• Publication Date: 2022-09-10
• Subjects: cut cotorsion pairs -- cut frobenius pairs -- cut Auslander-Buchweitz contexts; 18G25 -- 18G10 -- 18G20 -- 18G35 -- 18G80 -- 16E65; Mathematics -- Periodicals; 510
• DOI: 10.1017/S0017089521000367
• Languages: English
• ISSNs: 0017-0895

Abstract

Abstract: We present the concept of cotorsion pairs cut along subcategories of an abelian category. This provides a generalization of complete cotorsion pairs, and represents a general framework to find approximations restricted to certain subcategories. We also exhibit some connections between cut cotorsion pairs and Auslander–Buchweitz approximation theory, by considering relative analogs for Frobenius pairs and Auslander–Buchweitz contexts. Several applications are given in the settings of relative Gorenstein homological algebra, chain complexes, and quasi-coherent sheaves, as well as to characterize some important results on the Finitistic Dimension Conjecture, the existence of right adjoints of quotient functors by Serre subcategories, and the description of cotorsion pairs in triangulated categories as co- t -structures.