Frobenius $n$-exangulated categories

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 the 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. In addition, starting from n-exangulated categories, we obatin a new n-exangulated category. This construction gives n-exangulated categories which are neither n-exact categories nor (n + 2)-angulated categories. Finally, we discuss an application of main results and give some examples illustrating our main results.

The Grothendieck Group of an $n$-exangulated Category

“…(2) Let C be a Frobenius n-exangulated category, as recently defined in [10]. Then the subcategory P = I is both an n-generator and an n-cogenerator.…”

“…In [4,Section 6] several explicit examples of n-exangulated categories are given. See also [10,Section 4] for a construction which yields more nexangulated categories that are neither n-exact nor (n + 2)-angulated.…”