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 associatedconvolution algebra C_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 H-bundle P over G is uniquely determined by theassociated C_c(G)-C_c(H)-bimodule C_c(P) equipped with the natural coalgebrastructure. Furthermore, we prove that the functor C_c gives an equivalencebetween the Morita category of etale Lie groupoids and the Morita category oflocally grouplike Hopf algebroids.