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Given a compact quantum group $(G,\Delta)$, with dense Hopf algebra $H$, is it always true that, up to isomorphism, $H$ will have a countable number of irreducible comodules?

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Take a discrete uncountable group G of cardinality M, then $C^*_r(G)$ will be a compact quantum group with M irreducible (1-dimensional) corepresentations.

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