Tensor categories arising from the Virasoro algebra

We show that there is a braided tensor category structure on the of C 1 -cofinite modules for (universal or simple) Virasoro vertex operator algebras arbitrary central charge. In generic case charge c = 13 − 6 ( t + ) , with ∉ Q we prove semisimplicity, rigidity and non-degeneracy also compute fusion rules this category.