Categorical dualtiy for Yetter–Drinfeld C *

We develop a tensor categorical duality in the sprit of the Tannaka–Krein duality for the C * -algebras admitting the Yetter–Drinfeld module structure over a compact quantum group. Under this duality, given a reduced compact quantum group G , the Yetter–Drinfeld G -C * -algebras correspond to the bimodule categories over the representation category Rep ( G ) , satisfying a certain centrality condition.