The Drinfeld Centre of a Symmetric Fusion Category is 2-Fold Monoidal

Abstract

We show that the Drinfeld centre of a symmetric fusion category is a bilax 2-fold monoidal category. That is, it carries two monoidal structures, the convolution and symmetric tensor products, that are bilax monoidal functors with respect to each other. We additionally show that the braiding and symmetry for the convolution and symmetric tensor products are compatible with this bilax structure. We establish these properties without referring to Tannaka duality for the symmetric fusion category. This has the advantage that all constructions are done purely in terms of the fusion category structure, making the result easy to use in other contexts.

29 pages, many tikz-diagrams

References in corpus (4)

• The Symmetric Tensor Product on the Drinfeld Centre of a Symmetric Fusion Category
• The Elliptic Drinfeld Center of a Premodular Category
• Reduced Tensor Product on the Drinfeld Center
• Drinfeld Centre-Crossed Braided Tensor Categories

Cited by in corpus (6)

• Invertible braided tensor categories
• Reduced Tensor Product on the Drinfeld Center
• The Symmetric Tensor Product on the Drinfeld Centre of a Symmetric Fusion Category
• Drinfeld Centre-Crossed Braided Tensor Categories
• On the Category of Boundary Values in the Extended Crane-Yetter TQFT
• The Reduced Tensor Product of Braided Tensor Categories Containing a Symmetric Fusion Category