Frobenius $n$-exangulated categories

TL;DR

This paper introduces Frobenius $n$-exangulated categories, generalizing existing structures, and shows their stable categories form $(n+2)$-angulated categories, expanding the framework of higher homological algebra.

Contribution

It defines Frobenius $n$-exangulated categories, proves their stable categories are $(n+2)$-angulated, and provides examples outside previous classifications.

Findings

Stable categories of Frobenius $n$-exangulated categories are $(n+2)$-angulated.

The work generalizes Jasso's results on higher categories.

Provides examples of $n$-exangulated categories not fitting previous types.

Abstract

Herschend-Liu-Nakaoka introduced the notion of $n$-exangulated categories as higher dimensional analogues of extriangulated categories defined by Nakaoka-Palu. The class of $n$-exangulated categories contains $n$-exact categories and $(n+2)$-angulated categories as examples. In this article, we introduce a notion of Frobenius $n$-exangulated categories which are a generalization of Frobenius $n$-exact categories. We show that the stable category of a Frobenius $n$-exangulated category is an $(n+2)$-angulated category. As an application, this result generalizes the work by Jasso. We provide a class of $n$-exangulated categories which are neither $n$-exact categories nor $(n+2)$-angulated categories. Finally, we discuss an application of the main results and give some examples illustrating it.