论文标题
外侧类别的Grothendieck单体
Grothendieck monoids of extriangulated categories
论文作者
论文摘要
我们研究了外侧类别的Grothendieck Monoid（Grothendieck Group的单体版本），并给出一些结果，即使是Abelian类别也是新的。首先，我们使用Grothendieck Monoid对Serre子类别和3个子类别的密集分类进行了分类。其次，在良好的情况下，我们表明，外侧类别的定位的肉眼是对原始粒状himoid的天然商单体的同构。这包括Abelian类别的Serre商的案例和三角形类别的Verdier商。作为一个具体的示例，我们介绍了Abelian类别的派生类别的中间子类别，该类别位于Abelian类别及其一个转变之间。我们表明，中间子类别的族类别对应于Abelian类别中的Torsionfree类，然后计算中间子类别的Grothendieck Monoid。
We study the Grothendieck monoid (a monoid version of the Grothendieck group) of an extriangulated category, and give some results which are new even for abelian categories. First, we classify Serre subcategories and dense 2-out-of-3 subcategories using the Grothendieck monoid. Second, in good situations, we show that the Grothendieck monoid of the localization of an extriangulated category is isomorphic to the natural quotient monoid of the original Grothendieck monoid. This includes the cases of the Serre quotient of an abelian category and the Verdier quotient of a triangulated category. As a concrete example, we introduce an intermediate subcategory of the derived category of an abelian category, which lies between the abelian category and its one shift. We show that intermediate subcategories bijectively correspond to torsionfree classes in the abelian category, and then compute the Grothendieck monoid of an intermediate subcategory.
