The Morita Theory of Fusion 2-Categories
Abstract
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2022
- DOI:
- 10.48550/arXiv.2208.08722
- arXiv:
- arXiv:2208.08722
- Bibcode:
- 2022arXiv220808722D
- Keywords:
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- Mathematics - Category Theory;
- Mathematics - Quantum Algebra;
- 16D90;
- 18M20;
- 18N20;
- 18N25 (Primary);
- 18M30;
- 18N10 (Secondary)
- E-Print:
- Minor corrections