A new method to construct model structures from a cotorsion pair. Issue 11 (2nd November 2019)

• Record Type: Journal Article
• Authors: Chen, Wenjing; Liu, Zhongkui; Yang, Xiaoyan
• Is Part Of: Communications in algebra. Volume 47:Issue 11(2019)
• Page Start: 4420
• Page End: 4431
• Publication Date: 2019-11-02
• Subjects: Cotorsion pair -- Frobenius pair -- Gorenstein X-object -- model structure; 16E05 -- 18E10 -- 18E30; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2018.1527922
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: Let ( X, Y ) be a complete and hereditary cotorsion pair in an abelian category A . We show that if Y is closed under kernels of epimorphisms, then ( G ( X ) ∩ Y, X ∩ Y ) is a strong left Frobenius pair, which induces a unique projective exact model structure on ( G ( X ) ∩ Y ) ∧ . Some examples are given. Furthermore, we construct additional abelian model structures from ( X, Y ) and ( G ( X ), G ( X ) ⊥ ) .