Two results of $n$-exangulated categories

TL;DR

This paper advances the theory of $n$-exangulated categories by providing an equivalent axiom characterization and a novel method for constructing closed subfunctors, enhancing understanding of their structure.

Contribution

It offers a new characterization of the axiom (EA2) and introduces a method to construct closed subfunctors in $n$-exangulated categories, broadening their theoretical framework.

Findings

Equivalent characterization of axiom (EA2)

New construction method for closed subfunctors

Enhanced understanding of $n$-exangulated category structure

Abstract

$n$-exangulated categories were introduced by Herschend-Liu-Nakaoka which are a simultaneous generalization of $n$-exact categories and $(n+2)$-angulated categories. This paper consists of two results on $n$-exangulated categories: (1) we give an equivalent characterization of the axiom (EA2); (2) we provide a new way to construct a closed subfunctor of an $n$-exangulated category.