Coribbon Hopf (Face) Algebras Generated by Lattice Models

By studying “points of the underlying quantum groups” of coquasitriangular Hopf (face) algebras, we construct ribbon categories for each lattice models without spectral parameter of both vertex and face type. Also, we give a classification of the braiding and the ribbon structure on quantized classical groups and modular tensor categories closely related to quantum SU(N)L-invariants of 3-manifolds.