  For any finite group G with a finite G-set X and a modular tensor category C
we construct a part of the algebraic structure of an associated G-equivariant
monoidal category: For any group element g in G we exhibit the module category
structure of the g-component over the trivial component. This uses the
formalism of permutation equivariant modular functors that was worked out in
arXiv:1004.1825. As an application we show that the corresponding modular
invariant partition function is given by permutation by g.
