  Proposing a certain category of bialgebroid maps we show that the balanced
depth 2 extensions appear as they were the finitary Galois extensions in the
context of quantum groupoid actions, i.e., actions by finite bialgebroids, weak
bialgebras or weak Hopf algebras. We comment on deformation of weak bialgebras,
on half grouplike elements, on uniqueness of weak Hopf algebra reconstructions
and discuss the example of separable field extensions.
