  We will show a centrally free action of an amenable rigid C$^*$-tensor
category on a properly infinite von Neumann algebra has the Rohlin property.
This enables us to prove the fullness of the crossed product of a full factor
by minimal action of a compact group. As another application of the Rohlin
property, we will show the uniqueness of centrally free cocycle actions of an
amenable rigid C$^*$-tensor category on properly infinite von Neumann algebras.
