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?



Number of Isomorphism Classes of Corepresentations of A Compact Quantum Group
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.


