论文标题
分类图次要定理
The categorical graph minor theorem
论文作者
论文摘要
我们定义了图形次要类别，并证明了Noetherian环上图次要类别的违反表示的类别是本地Noetherian。这可以被视为罗伯逊（Robertson）的分类 - Seymour图次要定理。此外，我们将Sam和Snowden的Gröbner类别理论概括为由类别以及函子组成的对设置的设置，并将该理论应用于图形次要类别的Edge Fuctor。作为应用程序，我们研究了图形的无序配置空间的同源组，从而改善了该主题的各种有限生成。
We define the graph minor category and prove that the category of contravariant representations of the graph minor category over a Noetherian ring is locally Noetherian. This can be regarded as a categorification of the Robertson--Seymour graph minor theorem. In addition, we generalize Sam and Snowden's Gröbner theory of categories to the setting of pairs consisting of a category along with a functor to sets, and we apply this theory to the edge functor on the graph minor category. As an application, we study homology groups of unordered configuration spaces of graphs, improving upon various finite generation results in this subject.
