Abelian quotients of extriangulated categories

被引：2

作者：

He, Jing ^{[1
]}

Zhou, Panyue ^{[2
]}

机构：

[1] Cent South Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China

[2] Hunan Inst Sci & Technol, Coll Math, Yueyang 414006, Hunan, Peoples R China

来源：

PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES | 2019年 / 129卷 / 04期

关键词：

Extriangulated categories; abelian categories; cluster-tilting subcategories; TRIANGULATED CATEGORIES;

D O I：

10.1007/s12044-019-0492-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that certain subquotient categories of extriangulated categories are abelian. As a particular case, if an extriangulated category C has a cluster-tilting subcategory X, then C/X is abelian. This unifies a result by Koenig and Zhu (Math. Z. 258 (2008) 143-160) for triangulated categories and a result by Demonet and Liu (J. Pure Appl. Algebra 217(12) (2013) 2282-2297) for exact categories.

引用

页数：11

共 13 条

[1] APPLICATIONS OF CONTRAVARIANTLY FINITE SUBCATEGORIES [J].

AUSLANDER, M ;

REITEN, I .

ADVANCES IN MATHEMATICS, 1991, 86 (01) :111-152

[2] LEFT TRIANGULATED CATEGORIES ARISING FROM CONTRAVARIANTLY FINITE SUBCATEGORIES [J].

BELIGIANNIS, A ;

MARMARIDIS, N .

COMMUNICATIONS IN ALGEBRA, 1994, 22 (12) :5021-5036

[3]

Buan AB, 2007, T AM MATH SOC, V359, P323

[4] Tilting theory and cluster combinatorics [J].

Buan, Aslak Bakke ;

Marsh, Bethany Rose ;

Reineke, Markus ;

Reiten, Idun ;

Todorov, Gordana .

ADVANCES IN MATHEMATICS, 2006, 204 (02) :572-618

[5]

Chang W, 2016, ALGEBRAS REPRESENTAT

[6] Quotients of exact categories by cluster tilting subcategories as module categories [J].

Demonet, Laurent ;

Liu, Yu .

JOURNAL OF PURE AND APPLIED ALGEBRA, 2013, 217 (12) :2282-2297

[7]

Geiss C., 2008, Trends in Representation Theory of Algebras and Related Topics, EMS Series of Congress Reports, P253

[8] Rigid modules over preprojective algebras [J].

Geiss, Christof ;

Leclerc, Bernard ;

Schroeer, Jan .

INVENTIONES MATHEMATICAE, 2006, 165 (03) :589-632

[9] Mutation in triangulated categories and rigid Cohen-Macaulay modules [J].

Iyama, Osamu ;

Yoshino, Yuji .

INVENTIONES MATHEMATICAE, 2008, 172 (01) :117-168

[10] Cluster-tilted algebras are Gorenstein and stably Calabi-Yau [J].

Keller, Bernhard ;

Reiten, Idun .

ADVANCES IN MATHEMATICS, 2007, 211 (01) :123-151

← 1 2 →