n-angulated quotient categories induced by mutation pairs

TL;DR

This paper introduces mutation pairs in n-angulated categories and proves that their quotient categories inherit an n-angulated structure, generalizing classical results and extending to Frobenius n-angulated categories.

Contribution

It defines mutation pairs in n-angulated categories and shows their quotient categories are naturally n-angulated, extending Iyama-Yoshino's theorem to higher angulated settings.

Findings

Quotient categories of mutation pairs are n-angulated.

Frobenius n-angulated categories have n-angulated quotients.

Generalization of classical triangulated category results.

Abstract

We define mutation pair in an n-angulated category and prove that given such a mutation pair, the corresponding quotient category carries a natural n-angulated structure. This result generalizes a theorem of Iyama-Yoshino in classical triangulated category. As an application, we obtain that the quotient category of a Frobenius n-angulated category is also an n-angulated category.