Article
MSC:
16D90,
18M20,
18M30,
18N10,
18N20,
18N25 | MR 4600461 | Zbl 1534.18006 | DOI: 10.21136/HS.2023.07
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Keywords:
Fusion 2-Category; Morita Equivalence; Dual Tensor 2-Category; Morita 3-Category; Separable Module 2-Category
Fusion 2-Category; Morita Equivalence; Dual Tensor 2-Category; Morita 3-Category; Separable Module 2-Category
Summary:
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.
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