1. $n\mathbb{Z}$-abelian and $n\mathbb{Z}$-exact categories
- Author
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Ebrahimi, Ramin and Nasr-Isfahani, Alireza
- Subjects
Mathematics::Category Theory ,Mathematics - K-Theory and Homology ,FOS: Mathematics ,Mathematics - Category Theory ,Category Theory (math.CT) ,K-Theory and Homology (math.KT) ,18E99, 16E30 ,Representation Theory (math.RT) ,Mathematics - Representation Theory - 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.
- Published
- 2022
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