论文标题
球形莫里塔环境和相对serre函数
Spherical Morita contexts and relative Serre functors
论文作者
论文摘要
由有限张量类别的精确模块类别提供的莫里塔上下文提供了带有二元组的两对象bicategory。模块类别中对象的左右对偶分别由内部HOMS和COHOM给出。我们以相对Serre函子的形式表达双重双重双重，这导致了模块类别的Radford同构。 Radford $ s^4 $定理有一个生物版本：在莫里塔语境的生物学上，相对的Serre函数组装成伪函数，而Radford同构可提供该伪函数的平方的琐碎，即DAILS的四分之一动力。我们还表明，来自关键的精确模块类别的莫里塔（Morita）生物游戏作为生物游戏是关键的，导致了关键的莫里塔（Morita）等效性的概念。张量类别的这种等效性等于其关键模块类别的生物学的等效性。此外，我们介绍了球形模块类别的概念；它确保球形模块类别的莫里塔语境中的所有类别都是球形的。我们的结果是由拓扑领域理论的动机并应用了。
The Morita context provided by an exact module category over a finite tensor category gives a two-object bicategory with duals. Right and left duals of objects in the module category are given by internal Homs and coHoms, respectively. We express the double duals in terms of relative Serre functors, which leads to a Radford isomorphism for module categories. There is a bicategorical version of the Radford $S^4$ theorem: on the bicategory of a Morita context, the relative Serre functors assemble into a pseudo-functor, and the Radford isomorphisms furnish a trivialization of the square of this pseudo-functor, i.e. of the fourth power of the duals. We also show that the Morita bicategories coming from pivotal exact module categories are pivotal as bicategories, leading to the notion of pivotal Morita equivalence. This equivalence of tensor categories amounts to the equivalence of their bicategories of pivotal module categories. Furthermore, we introduce the notion of a spherical module category; it ensures that all categories in the Morita context of a spherical module category are spherical. Our results are motivated by and have applications to topological field theory.
