nℤ-ABELIAN AND nℤ-EXACT CATEGORIES

Abstract

In this paper, we introduce nℤ-abelian and nℤ-exact categories by axiomatizing properties of nℤ-cluster tilting subcategories. We study these categories and show that every nℤ-cluster tilting subcategory of an abelian (resp., exact) category has a natural structure of an nℤ-abelian (resp., nℤ-exact) category. Also, we show that every small nℤ-abelian category arises in this way, and discuss the problem for nℤ-exact categories. © The Author(s) 2023. Published by Oxford University Press. All rights reserved.