  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.
