$n\mathbb{Z}$-abelian and $n\mathbb{Z}$-exact categories

Ramin Ebrahimi; Alireza Nasr-Isfahani

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arXiv · 2202.06711

$n\mathbb{Z}$-abelian and $n\mathbb{Z}$-exact categories

Ramin Ebrahimi·Alireza Nasr-Isfahani

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Abstract

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

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BibTeX RIS

Ramin Ebrahimi, Alireza Nasr-Isfahani. 2022-02-14. $n\mathbb{Z}$-abelian and $n\mathbb{Z}$-exact categories. https://arxiv.org/abs/2202.06711

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