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In this paper, we generalize Izumi’s result on uniqueness of realization of finite C∗-tensor categories in the endomorphism category of the injective factor of type III1 for finitely generated strongly amenable C∗-tensor categories by applying Popa’s classification theorem of strongly amenable subfactors of type III1.

Classification of Roberts actions of strongly amenable C∗-tensor categories on the injective factor of type III1

Classification of Roberts actions of strongly amenable C∗-tensor categories on the injective factor of type III₁