The Tannaka-Krein duality for compact groups

The talk will be purely educational. We introduce some purely algebraic "dual objects" associated to any compact group. The key property of the objects is that the group can be completely reconstructed from any of them. In fact, there are at least two such objects, and for each of them we have a suitable "reconstruction theorem". We plan to discuss both theorems and to show that the Fourier transform establishes an equivalence between them.