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 CX, 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.