The Reduced Tensor Product of Braided Tensor Categories Containing a Symmetric Fusion Category

Abstract

We detail a construction of a symmetric monoidal structure, called the reduced tensor product on the 2-category of braided tensor categories $\mathbf{BTC}(\mathcal{A})$ containing a fixed symmetric fusion subcategory $\mathcal{A}$. The construction only depends on the braiding and monoidal structure of the categories involved. The main tool in the construction is an enriching procedure that is shown to give an equivalence between $\mathbf{BTC}(\mathcal{A})$ and a 2-category of so-called Drinfeld centre crossed braided tensor categories. As an application of the reduced tensor product, we show that it gives a pairing between minimal modular extensions of braided tensor categories containing $\mathcal{A}$ as their transparent subcategory.

arXiv comment48 pages, many diagrams

References in corpus (5)

• Fermionic Modular Categories and the 16-fold Way
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• Classification of 2+1D topological orders and SPT orders for bosonic and fermionic systems with on-site symmetries
• The Symmetric Tensor Product on the Drinfeld Centre of a Symmetric Fusion Category
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Cited by in corpus (2)

• The Symmetric Tensor Product on the Drinfeld Centre of a Symmetric Fusion Category
• Categorical Center of Higher Genera and 4D Factorization Homology