Hearts of twin cotorsion pairs on extriangulated categories

JOURNAL OF ALGEBRA

卷:528

Article

Liu, Yu¹  Nakaoka, Hiroyuki² 

[1] Southwest Jiaotong Univ, Sch Math, Chengdu 610051, Sichuan, Peoples R China

[2] Kagoshima Univ, Res Field Sci, Sci & Engn Area, Res & Educ Assembly, 1-21-35 Korimoto, Kagoshima 8900065, Japan

关键词: Extriangulated categories;    Cotorsion pairs;    Hearts;    n-cluster tilting subcategories;   

DOI  :  10.1016/j.jalgebra.2019.03.005

来源: Elsevier

【 摘 要 】

In this article, we study the heart of a cotorsion pairs on an exact category and a triangulated category in a unified method, by means of the notion of an extriangulated category. We prove that the heart is abelian, and construct a cohomo-logical functor to the heart. If the extriangulated category has enough projectives, this functor gives an equivalence between the heart and the category of coherent functors over the coheart modulo projectives. We also show how an n-cluster tilting subcategory of an extriangulated category gives rise to a family of cotorsion pairs with equivalent hearts. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free