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Title:
Finding braiding from a monoidal structure on Frobenius algebra objects
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Abstract:
It is well known that there is a monoidal structure on the algebra objects in a braided tensor category. The converse implication was pointed out in a recent work of Woronowicz in the framework of locally compact quantum groups and their actions on C*-algebras. We give a purely categorical counterpart to his result by a quite different looking proof. Namely, if C is a rigid tensor category, any monoidal structure on the Frobenius algebra objects in C corresponds to a braiding on C. This gives an intrinsic description of braiding on the representation categories of free automorphism quantum groups.
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