The Left and Right Triangulated Structures of Stable Categories

被引:2
作者
Li, Zhi-Wei [1 ]
机构
[1] Jiangsu Normal Univ, Sch Math & Stat, Xuzhou 221116, Jiangsu, Peoples R China
关键词
Abelian model category; Left triangulated category; Pretriangulated category; Stable category; HOMOTOPY-THEORY; MODULES;
D O I
10.1080/00927872.2014.923896
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Beligiannis and Marmaridis in 1994, constructed the one-sided triangulated structures on the stable categories of additive categories induced from some homologically finite subcategories. We extend their results to slightly more general settings. As an application of our results, we give some new examples of one-sided triangulated categories arising from abelian model categories. An interesting outcome is that we can describe the pretriangulated structures of the homotopy categories of abelian model categories via those of stable categories.
引用
收藏
页码:3725 / 3753
页数:29
相关论文
共 18 条
[1]  
[Anonymous], 1977, Lecture Notes in Math.
[2]   PREPROJECTIVE MODULES OVER ARTIN ALGEBRAS [J].
AUSLANDER, M ;
SMALO, SO .
JOURNAL OF ALGEBRA, 1980, 66 (01) :61-122
[3]   Models for singularity categories [J].
Becker, Hanno .
ADVANCES IN MATHEMATICS, 2014, 254 :187-232
[4]   LEFT TRIANGULATED CATEGORIES ARISING FROM CONTRAVARIANTLY FINITE SUBCATEGORIES [J].
BELIGIANNIS, A ;
MARMARIDIS, N .
COMMUNICATIONS IN ALGEBRA, 1994, 22 (12) :5021-5036
[5]  
Beligiannis A, 2001, MATH SCAND, V89, P5
[6]  
Beligiannis A, 2007, MEM AM MATH SOC, V188, P1
[7]   ABSTRACT HOMOTOPY THEORY AND GENERALIZED SHEAF COHOMOLOGY [J].
BROWN, KS .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1973, 186 (459) :419-458
[8]  
Dwyer W. G., 1995, HDB ALGEBRAIC TOPOLO
[9]  
Gabriel P., 1967, Calculus of Fractions and Homotopy Theory
[10]  
Gillespie J., ARXIV12100196