Dimensions and cotorsion pairs in recollements of extriangulated categories

被引：0

作者：

Ma, Xin ^{[1
]}

Zhou, Panyue ^{[2
]}

机构：

[1] Henan Univ Engn, Coll Sci, Zhengzhou, Henan, Peoples R China

[2] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410114, Hunan, Peoples R China

来源：

COMMUNICATIONS IN ALGEBRA | 2025年 / 53卷 / 01期

关键词：

Coresolution dimension; cotorsion pair; extriangulated category; recollement; TILTING SUBCATEGORIES; HEARTS;

D O I：

10.1080/00927872.2024.2374436

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let (A,B,C) be a recollement of extriangulated categories. In this paper, we provide bounds on the coresolution dimensions of the subcategories involved in A, B , and C . We show that a hereditary cotorsion pair in B can induce hereditary cotorsion pairs in A and C under certain conditions. Besides, we construct recollements of abelian categories from a recollement of extriangulated categories with respect to the hearts of cotorsion pairs.

引用

页码：242 / 258

页数：17

共 28 条

[1] Hereditary cotorsion pairs and silting subcategories in extriangulated categories [J].

Adachi, Takahide ;

Tsukamoto, Mayu .

JOURNAL OF ALGEBRA, 2022, 594 :109-137

[2]

Auslander M., 1995, Cambridge Stud. Adv. Math., V36

[3]

Belinson A. A., 1982, Astrisque, V100, P5

[4] Transport of structure in higher homological algebra [J].

Bennett-Tennenhaus, Raphael ;

Shah, Amit .

JOURNAL OF ALGEBRA, 2021, 574 :514-549

[5] COTORSION PAIRS IN A RECOLLEMENT OF TRIANGULATED CATEGORIES [J].

Chen, Jianmin .

COMMUNICATIONS IN ALGEBRA, 2013, 41 (08) :2903-2915

[6]

Franjou T., 2004, DOC MATH, V9, P41, DOI DOI 10.4171/DM/156

[7] The Recollements of Abelian Categories: Cotorsion Dimensions and Cotorsion Triples [J].

Fu, Xuerong ;

Hu, Yonggang .

BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2022, 48 (03) :963-977

[8]

Gorsky M., ARXIV

[9] Homological Dimensions of Extriangulated Categories and Recollements [J].

Gu, Weili ;

Ma, Xin ;

Tan, Lingling .

ALGEBRA COLLOQUIUM, 2023, 30 (04) :667-684

[10] Torsion pairs and recollements of extriangulated categories [J].

He, Jian ;

Hu, Yonggang ;

Zhou, Panyue .

COMMUNICATIONS IN ALGEBRA, 2022, 50 (05) :2018-2036

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