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Questions about algebraic structures known as quantum groups, and their categories of representations. Quasitriangular Hopf algebras and their Drinfel'd twists, triangular Hopf algebras, $C^\star$ quantum groups, h-adic quantum groups, various semisimplified categories at roots of unity which are called "quantum groups", bicrossproduct quantum groups, and quantum groups coming from braided tensor categories.

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Timmerman's "An invitation to quantum groups and duality" corollary 3.2.8

Everything is correct. First, suppose that the corepresentations are indeed irreducible. As you say, one of the implications follows from Prop. 3.2.6. For the opposite one: Suppose that $\mathop{\rm H …
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