On the existence of Auslander-Reiten (d+2)-angles in (d+2)-angulated categories

Abstract

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

16 pages. arXiv admin note: text overlap with arXiv:1910.01454

Cited by in corpus (3)

• Higher Auslander-Reiten sequences via morphisms determined by objects
• Auslander-Reiten-Serre duality for n-exangulated categories
• Grothendieck groups and Auslander-Reiten (d+2)-angles