Applications of hyperhomology to adjoint functors. Issue 1 (17th January 2022)

• Record Type: Journal Article
• Authors: Chen, Hongxing
• Is Part Of: Communications in algebra. Volume 50:Issue 1(2022)
• Page Start: 19
• Page End: 32
• Publication Date: 2022-01-17
• Subjects: Adjoint functor -- cotorsion pair -- homotopy category -- hyperhomology; Primary: 18G35 -- 18A40 -- 16G10 -- Secondary: 18G25 -- 16E05; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2021.1949019
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: Hyperhomology is applied to give explicit constructions of left or right adjoint functors of some inclusions between unbounded homotopy categories of additive categories arising from cotorsion pairs in abelian categories. These constructions are independent of Brown representability and do not involve cardinality in set theory. Applications are then given to injective cotorsion pairs in abelian categories and some typical cotorsion pairs in module categories of rings.