Strong Pedersen rigidity for coactions of compact groups

We prove a version of Pedersen's outer conjugacy theorem for coactions of compact groups, which characterizes outer conjugate coactions of a compact group in terms of properties of the dual actions. In fact, we show that every isomorphism of a dual action comes from a unique outer conjugacy of a coaction, which in this context should be called strong Pedersen rigidity. We promote this to a category equivalence.
Comment: 14 pages. Corrected confusion regarding the term "dual action", and added uniqueness clause to Pedersen's theorem. To appear in IJM