Equivalence between the Morita categories of etale Lie groupoids and of locally grouplike Hopf algebroids

摘要

Any etale Lie groupoid G is completely determined by its associated convolution algebra C°(G) equipped with the natural Hopf algebroid structure We extend this result to the generalized morphisms between etale Lie groupoids: we show that any principal #-bundle P over G is uniquely determined by the associated C (G)-C°(H )-bimodu(P) equipped with the natural coalgebra structure Furthermore, we prove that the functor C° gives an equivalence between the Morita category of etale Lie groupoids and the Morita category of locally grouplike Hopf algebroids.