Tannaka–Krein duality for compact quantum groups is a theorem that generalizes the classical Tannaka–Krein duality for compact groups. Basic idea of the theorem is that any compact quantum group can be recovered from its representation theory (i.e. from the structure of the category of its representations).

There are several possibilities, how to formulate this result, which differ in their generality and in the amount of categorical formulations involved. Here, we present some of them starting with the most abstract one and going more concrete.