论文标题
小组分区类别
Group partition categories
论文作者
论文摘要
对于每个组$ g $，我们将线性单体类别$ \ MATHCAL {p} \ MATHIT {ar}（g）$关联，我们称为组分区类别。我们为形态空间提供明确的基础，并在发电机和关系方面有效地呈现类别。然后，我们将$ \ Mathcal {p} \ Mathit {ar}（g）$的嵌入到与$ g $相关的Heisenberg类别中。这将两种类别的自然作用交织在模块上的自然作用中，用于$ g $的花圈产品。最后，我们证明了$ \ Mathcal {p} \ Mathit {ar}（g）$的添加剂karoubi信封$等同于诺普（Knop）引入的花圈产品插值类别，从而对该类别进行了简单的具体描述。
To every group $G$ we associate a linear monoidal category $\mathcal{P}\mathit{ar}(G)$ that we call a group partition category. We give explicit bases for the morphism spaces and also an efficient presentation of the category in terms of generators and relations. We then define an embedding of $\mathcal{P}\mathit{ar}(G)$ into the group Heisenberg category associated to $G$. This embedding intertwines the natural actions of both categories on modules for wreath products of $G$. Finally, we prove that the additive Karoubi envelope of $\mathcal{P}\mathit{ar}(G)$ is equivalent to a wreath product interpolating category introduced by Knop, thereby giving a simple concrete description of that category.
