One-sided Frobenius pairs in extriangulated categories. Issue 12 (2nd December 2022)

• Record Type: Journal Article
• Authors: Tan, Lingling; Gao, Yuqiong; Chen, Qinghua
• Is Part Of: Communications in algebra. Volume 50:Issue 12(2022)
• Page Start: 5345
• Page End: 5370
• Publication Date: 2022-12-02
• Subjects: A proper class of E-triangles -- Extriangulated categories -- left Frobenius pairs -- left n-cotorsion pairs -- left (weak) Auslander-Buchweitz contexts; 18G20 -- 18G25; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2022.2084748
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: Let C be an extriangulated category with a proper class ξ of E -triangles. We introduce the notions of left Frobenius pairs, left ( n -)cotorsion pairs and left (weak) Auslander-Buchweitz contexts with respect to ξ in C . We show how to construct left cotorsion pais from left n -cotorsion pairs, and establish a one-to-one correspondence between left Frobenius pairs and left (weak) Auslander-Buchweitz contexts. We also study the relation between a certain class of cotorsion pairs and that of n -cotorsion pairs. These work generalize Ma-Zhao-Huang's results in triangulated categories and partially generalize Becerril-Mendoza-Pérez-Santiago's results in abelian categories.