1. nℤ-abelian and nℤ-exact categories.
- Author
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Ebrahimi, Ramin and Nasr-Isfahani, Alireza
- Subjects
CLUSTER algebras ,ABELIAN categories - Abstract
In this paper, we introduce |$n\mathbb{Z}$| -abelian and |$n\mathbb{Z}$| -exact categories by axiomatizing properties of |$n\mathbb{Z}$| -cluster tilting subcategories. We study these 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 arises in this way, and discuss the problem for |$n\mathbb{Z}$| -exact categories. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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