Ideal approximation in $n$-angulated categories

TL;DR

This paper extends ideal approximation theory to almost $n$-exact structures within extension closed subcategories of $n$-angulated categories, generalizing existing theories from triangulated and exact categories.

Contribution

It introduces a new framework for ideal approximation in $n$-angulated categories, broadening the scope of prior theories from triangulated and exact categories.

Findings

Develops ideal approximation theory for $n$-angulated categories.

Connects $n=3$ case to classical triangulated categories.

Extends existing theories to a more general $n$-angulated setting.

Abstract

In this paper, we study ideal approximation theory associated to almost $n$-exact structures in extension closed subcategories of $n$-angulated categories. For $n=3$, an $n$-angulated category is nothing but a classical triangulated category. Moreover, since every exact category can be embedded as an extension closed subcategory of a triangulated category, therefore, our approach extends the recent ideal approximations theories developed by Fu, Herzog et al. for exact categories and by Breaz and Modoi for triangulated categories.