A complete classification of 2d symmetry protected states with symmetric entanglers

We consider symmetry protected topological states of 2d quantum spin systems, with a finite symmetry group G. It has been conjectured that such states are classified by the cohomology group H^3(G,U(1)), but the completeness of this classification is an open problem. We restrict ourselves to symmetry protected topological states that can be prepared from a product state by a symmetric entangler. For this class of states, we prove that the classification by H^3(G,U(1)) is complete.