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We prove a version of Pedersen's outer conjugacy theorem for coactions ofcompact groups, which characterizes outer conjugate coactions of a compactgroup in terms of properties of the dual actions. In fact, we show that everyisomorphism of a dual action comes from a unique outer conjugacy of a coaction,which in this context should be called strong Pedersen rigidity. We promotethis to a category equivalence.

Strong Pedersen rigidity for coactions of compact groups