N-extension closed subcategories of (n+2)-angulated categories

TL;DR

This paper demonstrates that certain subcategories of (n+2)-angulated categories naturally inherit an n-exangulated structure, expanding the understanding of their categorical properties and providing new examples beyond existing frameworks.

Contribution

It establishes that n-extension closed subcategories of (n+2)-angulated categories are n-exangulated, introducing new structures not covered by previous n-exact or (n+2)-angulated categories.

Findings

Subcategories inherit n-exangulated structure

Provides examples beyond n-exact and (n+2)-angulated categories

Enables applications to recent main results in the field

Abstract

Let $\mathscr C$ be a Krull-Schmidt $(n+2)$-angulated category and $\mathscr A$ be an $n$-extension closed subcategory of $\mathscr C$. Then $\mathscr A$ has the structure of an $n$-exangulated category in the sense of Herschend-Liu-Nakaoka. This construction gives $n$-exangulated categories which are not $n$-exact categories in the sense of Jasso nor $(n+2)$-angulated categories in the sense of Geiss-Keller-Oppermann in general. As an application, our result can lead to a recent main result of Klapproth.