A new characterization of n-exangulated categories with (n+2)-angulated structure

TL;DR

This paper characterizes when n-exangulated categories can be endowed with an (n+2)-angulated structure, linking these concepts through conditions on trivial deflations and inflations.

Contribution

It provides a necessary and sufficient condition for n-exangulated categories to admit an (n+2)-angulated structure, unifying higher categorical frameworks.

Findings

n-exangulated categories have (n+2)-angulated structure iff certain morphisms are trivial

The work generalizes and connects multiple higher categorical concepts

Provides a criterion for structural enhancement of n-exangulated categories

Abstract

Herschend-Liu-Nakaoka introduced the notion of $n$-exangulated categories. It is not only a higher dimensional analogue of extriangulated categories defined by Nakaoka-Palu, but also gives a simultaneous generalization of $(n+2)$-angulated in the sense of Geiss-Keller-Oppermann and $n$-exact categories in the sense of Jasso. In this article, we show that an $n$-exangulated category has the structure of an $(n+2)$-angulated category if and only if for any object $X$ in the category, the morphism $0\to X$ is a trivial deflation and the morphism $X\to 0$ is a trivial inflation.