Localization of n-exangulated categories

TL;DR

This paper establishes conditions under which localizing an n-exangulated category results in another n-exangulated category, expanding the understanding of higher-dimensional categorical structures and unifying various quotient constructions.

Contribution

It provides a necessary and sufficient condition for the localization of an n-exangulated category to remain n-exangulated, introducing new classes of such categories beyond existing frameworks.

Findings

Derived a criterion for n-exangulated localizations

Identified new classes of n-exangulated categories

Generalized previous localization results

Abstract

Nakaoka-Ogawa-Sakai considered the localization of an extriangulated category. This construction unified the Serre quotient of abelian categories and the Verdier quotient of triangulated categories. Recently, Herschend-Liu-Nakaoka defined $n$-exangulated categories as a higher dimensional analogue of extriangulated categories. Let $\mathcal C$ be an $n$-exangulated category and $\mathcal{F}$ be a multiplicative system satisfying mild assumption. In this article, we give a necessary and sufficient condition for the localization of $\mathcal C$ be an $n$-exangulated category. This way gives a new class of $n$-exangulated categories which are neither $n$-exact nor $(n+2)$-angulated in general. Moreover, our result also generalizes work by Nakaoka-Ogawa-Sakai.