$n\mathbb{Z}$-abelian and $n\mathbb{Z}$-exact categories
Category Theory
2022-02-15 v1 K-Theory and Homology
Representation Theory
Abstract
In this paper we introduce -abelian and -exact categories by axiomatising properties of -cluster tilting subcategories. We study this categories and show that every -cluster tilting subcategory of an abelian (resp., exact) category has a natural structure of an -abelian (resp., -exact) category. Also we show that every small -abelian category arise in this way, and discuss the problem for -exact categories.
Cite
@article{arxiv.2202.06711,
title = {$n\mathbb{Z}$-abelian and $n\mathbb{Z}$-exact categories},
author = {Ramin Ebrahimi and Alireza Nasr-Isfahani},
journal= {arXiv preprint arXiv:2202.06711},
year = {2022}
}