论文标题
莫里塔融合2类的理论
The Morita Theory of Fusion 2-Categories
论文作者
论文摘要
我们发展了莫里塔融合2类的理论。为了做到这一点，我们首先证明了在融合2类中存在可分离代数上的模块的相对张量产物。我们使用此结果来构建融合2类中可分离代数的Morita 3类。然后，我们继续解释模块2类别如何形成3类。之后，我们将可分开的模块定义为2类别，并证明可分离代数的莫里塔3类别等于3类可分离模块2类别。结果，我们表明，相对于可分开的模块2类别（即模块2类函数的2类），双张量2类是一个多fusion 2类别。最后，我们给出了融合2类之间的莫里塔等效性的三个等效特征。
We develop the Morita theory of fusion 2-categories. In order to do so, we begin by proving that the relative tensor product of modules over a separable algebra in a fusion 2-category exists. We use this result to construct the Morita 3-category of separable algebras in a fusion 2-category. Then, we go on to explain how module 2-categories form a 3-category. After that, we define separable module 2-categories over a fusion 2-category, and prove that the Morita 3-category of separable algebras is equivalent to the 3-category of separable module 2-categories. As a consequence, we show that the dual tensor 2-category with respect to a separable module 2-category, that is the associated 2-category of module 2-endofunctors, is a multifusion 2-category. Finally, we give three equivalent characterizations of Morita equivalence between fusion 2-categories.
