One-sided n-suspended categories

TL;DR

This paper introduces the concept of one-sided n-suspended categories, generalizing existing n-angled and n-exact categories, and provides methods to construct n-angulated quotient categories within this framework.

Contribution

It generalizes previous concepts by defining one-sided n-suspended categories and offers a framework to derive n-angulated categories and quotient constructions.

Findings

Introduces one-sided n-suspended categories as a unifying framework.

Provides a method to pass from n-suspended to n-angulated categories.

Constructs n-angulated quotient categories from Frobenius n-prile categories.

Abstract

Let $n$ be an integer greater or equal than $3$. We give a simultaneous generalization of $(n-2)$-exact categories and $n$-angulated categories, and we call it one-sided $n$-suspended categories. One-sided $n$-angulated categories are also examples of one-sided $n$-suspended categories. We provide a general framework for passing from one-sided $n$-suspended categories to one-sided $n$-angulated categories. Besides, we give a method to construct $n$-angulated quotient categories from Frobenius $n$-prile categories. These results generalize their works by Jasso for $n$-exact categories, Lin for $(n+2)$-angulated categories and Li for one-sided suspended categories.