Open Access
April, 2021 On the Existence of Auslander-Reiten $(d+2)$-angles in $(d+2)$-angulated Categories
Panyue Zhou
Author Affiliations +
Taiwanese J. Math. 25(2): 233-249 (April, 2021). DOI: 10.11650/tjm/201102


Let $\mathcal{C}$ be a $(d+2)$-angulated category. In this note, we show that if $\mathcal{C}$ is locally finite, then $\mathcal{C}$ has Auslander-Reiten $(d+2)$-angles. This extends a result of Xiao and Zhu for triangulated categories.

Funding Statement

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11901190 and 11671221), and by the Hunan Provincial Natural Science Foundation of China (Grant No. 2018JJ3205), and by the Scientific Research Fund of Hunan Provincial Education Department (Grant No. 19B239).


The author is highly grateful to the referee for his/her valuable comments and suggestions which led to improvements of this paper. He also would like to thank Professor Hailou Yao for his assistance in an earlier version of this work.


Download Citation

Panyue Zhou. "On the Existence of Auslander-Reiten $(d+2)$-angles in $(d+2)$-angulated Categories." Taiwanese J. Math. 25 (2) 233 - 249, April, 2021.


Received: 14 January 2020; Revised: 27 October 2020; Accepted: 19 November 2020; Published: April, 2021
First available in Project Euclid: 24 March 2021

Digital Object Identifier: 10.11650/tjm/201102

Primary: 16G70 , 18G80

Keywords: $(d+2)$-angulated category , Auslander-Reiten $(d+2)$-angle , locally finite

Rights: Copyright © 2021 The Mathematical Society of the Republic of China

Vol.25 • No. 2 • April, 2021
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