Goodness in $n$-angulated categories

TL;DR

This paper extends the concepts of good morphisms from triangulated categories to $n$-angulated categories and proves a key property for morphisms in certain $n$-angulated categories.

Contribution

It generalizes the notions of good morphisms to $n$-angulated categories and establishes that all morphisms of $n$-angles are middling good in specific categories.

Findings

All morphisms of $n$-angles are middling good for $n>3$.

Generalization of morphism properties from triangulated to $n$-angulated categories.

Provides foundational results for the structure of $n$-angulated categories.

Abstract

We generalise the notions of good, middling good, and Verdier good morphisms of distinguished triangles in triangulated categories, first introduced by Neeman, to the setting of $n$-angulated categories, introduced in Geiss, Keller, and Oppermann. We then prove that all morphisms of $n$-angles in an $(n-2)$-cluster tilting $n$-angulated category are middling good for $n>3$.