n-exangulated categories (I): Definitions and fundamental properties

被引：42

作者：

Herschend, Martin ^{[1
]}

Liu, Yu ^{[2
]}

Nakaoka, Hiroyuki ^{[3
]}

机构：

[1] Uppsala Univ, Dept Math, Box 480, S-75106 Uppsala, Sweden

[2] Southwest Jiaotong Univ, Sch Math, Chengdu 610031, Sichuan, Peoples R China

[3] Nagoya Univ, Grad Sch Math, Chikusa Ku, Furo Cho, Nagoya, Aichi 4648602, Japan

来源：

JOURNAL OF ALGEBRA | 2021年 / 570卷

基金：

中国国家自然科学基金; 瑞典研究理事会;

关键词：

Triangulated category; Exact category; n-angulated category; n-exact category;

D O I：

10.1016/j.jalgebra.2020.11.017

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For each positive integer n we introduce the notion of n-exangulated categories as higher dimensional analogues of extriangulated categories defined by Nakaoka-Palu. We characterize which n-exangulated categories are n-exact in the sense of Jasso and which are (n 2)-angulated in the sense of Geiss-Keller-Oppermann. (C) 2020 Elsevier Inc. All rights reserved.

引用

页码：531 / 586

页数：56

共 21 条

[11] Higher-dimensional Auslander-Reiten theory on maximal orthogonal subcategories [J].

Iyama, Osamu .

ADVANCES IN MATHEMATICS, 2007, 210 (01) :22-50

[12] n-REPRESENTATION-FINITE ALGEBRAS AND n-APR TILTING [J].

Iyama, Osamu ;

Oppermann, Steffen .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2011, 363 (12) :6575-6614

[13] Cluster tilting for higher Auslander algebras [J].

Iyama, Osamu .

ADVANCES IN MATHEMATICS, 2011, 226 (01) :1-61

[14]

Jasso G., ARXIV160403473

[15] n-Abelian and n-exact categories [J].

Jasso, Gustavo .

MATHEMATISCHE ZEITSCHRIFT, 2016, 283 (3-4) :703-759

[16]

Lane SaundersMac., 1995, CLASSICS MATH

[17] Hearts of twin cotorsion pairs on extriangulated categories [J].

Liu, Yu ;

Nakaoka, Hiroyuki .

JOURNAL OF ALGEBRA, 2019, 528 :96-149

[18]

Luo DR, 2017, P INDIAN AS-MATH SCI, V127, P625, DOI 10.1007/s12044-017-0345-4

[19]

Nakaoka H., 2019, CAH TOPOL GEOM DIFFE, V60, P117

[20] Tensor products of n-complete algebras [J].

Pasquali, Andrea .

JOURNAL OF PURE AND APPLIED ALGEBRA, 2019, 223 (08) :3537-3553

← 1 2 3 →