Motivated by the earlier work of Kac-Wakimoto on the coset constructions associated with affine vertex operator algebras, the categorial coset constructions are investigated and Kac-Wakimoto Hypothesis is proved under some mild conditions. In particular, the field identifications are obtained. These results are applied to the coset constructions in the theory of vertex operator algebras. This is a joint work with C.Dong and F.Xu.