Abstract
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).
Acknowledgments
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.
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. https://doi.org/10.11650/tjm/201102
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