ALMOST SPLIT TRIANGLES IN PRE-EXTRIANGULATED CATEGORIES

被引：0

作者：

Tan, Lingling ^{[1
]}

Wang, Dingguo ^{[1
]}

Zhao, Tiwei ^{[1
]}

机构：

[1] Qufu Normal Univ, Sch Math Sci, Qufu 273165, Shandong, Peoples R China

来源：

COLLOQUIUM MATHEMATICUM | 2023年 / 171卷 / 02期

关键词：

pre-extriangulated categories; almost split s-triangles; extension-closed subcategories; approximations; TWIN COTORSION PAIRS; REPRESENTATION THEORY; ARTIN ALGEBRAS; HEARTS;

D O I：

10.4064/cm8781-5-2022

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the notion of pre-extriangulated categories. We give some characterizations of almost split s-triangles in a pre-extriangulated category and provide necessary and sufficient conditions for the existence of such triangles. If E is an extension-closed subcategory of a pre-extriangulated category C having almost split s-triangles, we obtain necessary and sufficient conditions for E to have almost split s-triangles using the approximation properties of a certain class of objects.

引用

页码：189 / 209

页数：21

共 26 条

[1] [Anonymous], 1995, CAMBRIDGE STUD ADV M
[2] Assem I., 2006, ELEMENTS REPRESENTAT, V65
[3] REPRESENTATION THEORY OF ARTIN ALGEBRAS -3 ALMOST SPLIT SEQUENCES
AUSLANDER, M
REITEN, I
[J]. COMMUNICATIONS IN ALGEBRA, 1975, 3 (03) : 239 - 294
[4] REPRESENTATION THEORY OF ARTIN ALGEBRAS .4. INVARIANTS GIVEN BY ALMOST SPLIT SEQUENCES
AUSLANDER, M
REITEN, I
[J]. COMMUNICATIONS IN ALGEBRA, 1977, 5 (05) : 443 - 518
[5] Cluster Subalgebras and Cotorsion Pairs in Frobenius Extriangulated Categories
Chang, Wen
Zhou, Panyue
Zhu, Bin
[J]. ALGEBRAS AND REPRESENTATION THEORY, 2019, 22 (05) : 1051 - 1081
[6] Exact categories and vector space categories
Draxler, P
Reiten, I
Smalo, SO
Solberg, O
Keller, B
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1999, 351 (02) : 647 - 682
[7] Ideal approximation theory
Fu, X. H.
Asensio, P. A. Guil
Herzog, I.
Torrecillas, B.
[J]. ADVANCES IN MATHEMATICS, 2013, 244 : 750 - 790
[8] Happel D., 1988, TRIANGULATED CATEGOR, V119
[9] Herschend M, 2018, Arxiv, DOI arXiv:1709.06689
[10] Proper resolutions and Gorensteinness in extriangulated categories
Hu, Jiangsheng
Zhang, Dondong
Zhou, Panyue
[J]. FRONTIERS OF MATHEMATICS IN CHINA, 2021, 16 (01) : 95 - 117

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