论文标题
$ n \ mathbb {z} $ - abelian和$ n \ mathbb {z} $ - 精确类别
$n\mathbb{Z}$-abelian and $n\mathbb{Z}$-exact categories
论文作者
论文摘要
在本文中，我们介绍了$ n \ mathbb {z} $ - abelian和$ n \ mathbb {z} $ - 通过$ n \ mathbb {z} $的axiomatising属性的确切类别 - 群集倾斜子类别。我们研究此类别并表明，每一个$ n \ mathbb {z} $ - abelian（resp。centerry）类别的集群倾斜子类别具有$ n \ mathbb {z} $ - abelian的自然结构（resp。另外，我们还表明，每个小$ n \ mathbb {z} $ - Abelian类别以这种方式出现，并讨论$ n \ mathbb {z} $ - 精确类别的问题。
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.
