Quantum principal bundles and Tannaka-Krein duality theory

The structure of quantum principal bundles is studied, from the viewpoint of Tannaka-Krein duality theory. It is shown that if the structure quantum group is compact, principal G-bundles over a quantum space M are in a natural correspondence with certain contravariant functors defined on the category of finite-dimensional unitary representations of G, with the values in the category of finite projective bimodules over a ∗-algebra representing the base space.