论文标题
统一的伪自然变换
Unitary pseudonatural transformations
论文作者
论文摘要
我们建议对单位伪匕首在2类中的单一伪函数之间进行假性转换的定义的定义两种方法。首先是要求转换的2型成分是统一的。第二个是要求转换的匕首等于其反向。我们表明，使这些定义等效的“反向”是伪函数c-> d的2类娱乐（c，d）中转换的正确双重，伪自然变换和修改。我们表明，子类别fun_u（c，d）$ \ subset $ fun（c，d），其对象是单一的假函数，其1年形式是单一的伪自然转换，这是一个关键的匕首2类别。我们应用这些结果来获得莫里塔理论分类，该分类是纤维函子之间在紧凑型量子组的表示类别上单位伪函数之间的统一伪自然变换。
We suggest two approaches to a definition of unitarity for pseudonatural transformations between unitary pseudofunctors on pivotal dagger 2-categories. The first is to require that the 2-morphism components of the transformation be unitary. The second is to require that the dagger of the transformation be equal to its inverse. We show that the `inverse' making these definitions equivalent is the right dual of the transformation in the 2-category Fun(C,D) of pseudofunctors C -> D, pseudonatural transformations, and modifications. We show that the subcategory Fun_u(C,D) $\subset$ Fun(C,D) whose objects are unitary pseudofunctors and whose 1-morphisms are unitary pseudonatural transformations is a pivotal dagger 2-category. We apply these results to obtain a Morita-theoretical classification of unitary pseudonatural transformations between fibre functors on the category of representations of a compact quantum group.
