The Symmetric Tensor Product on the Drinfeld Centre of a Symmetric Fusion Category

Understand

We define a symmetric tensor product on the Drinfeld centre of a symmetric fusion category, in addition to its usual tensor product.

• We examine what this tensor product looks like under Tannaka duality, identifying the symmetric fusion category with the representation category of a finite (super)-group.
• Under this identification, the Drinfeld centre is the category of equivariant vector bundles over the finite group (underlying the super-group, in the super case).
• In the non-super case, we show that the symmetric tensor product corresponds to the fibrewise tensor product of these vector bundles.