论文标题
Abelian类别的Axiomatization子类别
Axiomatizing Subcategories of Abelian Categories
论文作者
论文摘要
我们研究了如何根据内在公理来表征阿贝尔类别的子类别。特别是，我们发现固有的公理表征，这些公理表征了生成有限的子类别，群集的倾斜子类别以及群集倾斜亚比类别的子类别。结果，我们证明，任何$ d $ -Abelian类别都等同于Abelian类别的$ D $ - 集群倾斜子类别，而没有对正在投影生成的类别的任何假设。
We investigate how to characterize subcategories of abelian categories in terms of intrinsic axioms. In particular, we find intrinsic axioms which characterize generating cogenerating functorially finite subcategories, precluster tilting subcategories, and cluster tilting subcategories of abelian categories. As a consequence we prove that any $d$-abelian category is equivalent to a $d$-cluster tilting subcategory of an abelian category, without any assumption on the categories being projectively generated.
