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.

中文翻译：

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对称融合范畴的 Drinfeld 中心是 2 重幺半群

我们证明了对称融合类别的 Drinfeld 中心是一个 bilax 2-fold monoidal 类别。也就是说，它带有两个幺半群结构，即卷积和对称张量积，它们是彼此相关的双单群函子。我们还表明，卷积和对称张量积的编织和对称性与这种 bilax 结构兼容。我们在不参考对称融合类别的 Tannaka 对偶性的情况下建立这些属性。这样做的优点是所有的构造都是纯粹根据融合类别结构完成的，使得结果易于在其他上下文中使用。