Hearts of twin cotorsion pairs on extriangulated categories

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 cohomological functor to the heart. If the extriangulated category...

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Bibliographic Details
Published inJournal of algebra Vol. 528; pp. 96 - 149
Main Authors Liu, Yu, Nakaoka, Hiroyuki
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.06.2019
Subjects
Cotorsion pairs
Extriangulated categories
Hearts
n-cluster tilting subcategories
18E10
18E30
Hearts
n-cluster tilting subcategories
16G99
Extriangulated categories
Cotorsion pairs
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Summary: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 cohomological 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.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2019.03.005