论文标题
歧管张量类别
Manifold tensor categories
论文作者
论文摘要
我们介绍了歧管张量类别，这些类别具有具有简单对象的歧管的张量类别的概念。一个基本示例是由谎言组分级的向量空间类别。与经典的张量类别理论不同，我们的设置跟踪简单对象的流形的平滑（和拓扑）结构。我们为流形张量类别设置了必要的定义，并将其称为Orbifold Tensor类别的概括。我们还构建了许多示例，最著名的是两个示例家庭，我们称为插值tambara-yamagami类别和插值量子组类别。最后，我们显示了条件下，Orbifold Tensor类别中的双重二元性数据会自动组装成平滑的二元性数据。我们的证明使用差异几何形状的经典隐式函数定理。
We introduce Manifold tensor categories, which make precise the notion of a tensor category with a manifold of simple objects. A basic example is the category of vector spaces graded by a Lie group. Unlike classic tensor category theory, our setup keeps track of the smooth (and topological) structure of the manifold of simple objects. We set down the necessary definitions for Manifold tensor categories and a generalisation we term Orbifold tensor categories. We also construct a number of examples, most notably two families of examples we call Interpolated Tambara-Yamagami categories and Interpolated quantum group categories. Finally, we show conditions under which pointwise duality data in an Orbifold tensor category automatically assembles into smooth duality data. Our proof uses the classic Implicit function theorem from differential geometry.
