English

$n\mathbb{Z}$-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 nZn\mathbb{Z}-abelian and nZn\mathbb{Z}-exact categories by axiomatising properties of nZn\mathbb{Z}-cluster tilting subcategories. We study this categories and show that every nZn\mathbb{Z}-cluster tilting subcategory of an abelian (resp., exact) category has a natural structure of an nZn\mathbb{Z}-abelian (resp., nZn\mathbb{Z}-exact) category. Also we show that every small nZn\mathbb{Z}-abelian category arise in this way, and discuss the problem for nZn\mathbb{Z}-exact categories.

Keywords

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}
}
R2 v1 2026-06-24T09:35:17.647Z