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

TL;DR

This paper proves that locally finite (d+2)-angulated categories always contain Auslander-Reiten (d+2)-angles, extending known results from triangulated categories to a broader class.

Contribution

It establishes the existence of Auslander-Reiten (d+2)-angles in locally finite (d+2)-angulated categories, generalizing previous results from triangulated categories.

Findings

Existence of Auslander-Reiten (d+2)-angles in locally finite (d+2)-angulated categories

Extension of Xiao-Zhu's result from triangulated to (d+2)-angulated categories

Provides foundational results for the structure theory of (d+2)-angulated categories

Abstract

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