2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/209516Any etale Lie groupoid G is completely determined by its associated convolution 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 the associated C_c(G)-C_c(H)-bimodule C_c(P) equipped with the natural coalgebra structure. Furthermore, we prove that the functor C_c gives an equivalence between the Morita category of etale Lie groupoids and the Morita category of locally grouplike Hopf algebroids.19 pagesQuantum AlgebraDifferential GeometryOperator Algebras16W30; 22A22text