$n$-exangulated categories

TL;DR

This paper introduces $n$-exangulated categories as higher-dimensional generalizations of extriangulated categories, characterizes their special cases, and explores their relation to $n$-cluster tilting subcategories.

Contribution

It defines $n$-exangulated categories, characterizes when they are $n$-exact or $(n+2)$-angulated, and links $n$-cluster tilting subcategories to $n$-exangulated structures.

Findings

Characterization of $n$-exangulated categories as $n$-exact or $(n+2)$-angulated.

Identification of conditions under which $n$-cluster tilting subcategories are $n$-exangulated.

Extension of extriangulated categories to higher dimensions.

Abstract

For each positive integer $n$ we introduce the notion of $n$-exangulated categories as higher dimensional analogues of extriangulated categories defined by Nakaoka-Palu. We characterize which $n$-exangulated categories are $n$-exact in the sense of Jasso and which are $(n+2)$-angulated in the sense of Geiss-Keller-Oppermann. For extriangulated categories with enough projectives and injectives we introduce the notion of $n$-cluster tilting subcategories and show that under certain conditions such $n$-cluster tilting subcategories are $n$-exangulated.