  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.
