  Let G be a finite group. Given a finite G-set X and a modular tensor category
C, we construct a weak G-equivariant fusion category, called the permutation
equivariant tensor category. The construction is geometric and uses the
formalism of modular functors. As an application, we concretely work out a
complete set of structure morphisms for Z/2-permutation equivariant categories,
finishing thereby a program we initiated in an earlier paper arXiv:0812.0986
[math.CT].
