酉伪自然变换
Unitary pseudonatural transformations
AI总结：
本文定义并刻画 pivotal dagger 2-范畴中酉伪函子间的酉伪自然变换，证明酉伪函子与酉伪自然变换构成 pivotal dagger 2-范畴，并用于分类紧量子群纤维函子间的变换。
摘要：
我们提出了两种方法，用于定义 pivotal dagger 2-范畴上酉伪函子之间伪自然变换的酉性。第一种要求变换的 2-态射分量是酉的。第二种要求变换的 dagger 等于其逆。我们证明，使这些定义等价的“逆”是变换在 2-范畴 Fun(C,D) 中的右对偶，该范畴由伪函子 C -> D、伪自然变换和修正组成。我们证明，对象为酉伪函子、1-态射为酉伪自然变换的子范畴 Fun_u(C,D) ⊂ Fun(C,D) 是一个 pivotal dagger 2-范畴。我们应用这些结果，对紧量子群表示范畴上纤维函子之间的酉伪自然变换给出了 Morita 理论分类。
英文摘要：
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.
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