2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/99192We give the construction of a class of weak Hopf algebras (or quantum groupoids) associated to a matched pair of groupoids and certain cocycle data. This generalizes a now well-known construction for Hopf algebras, first studied by G. I. Kac in the sixties. Our approach is based on the notion of double groupoids, as introduced by Ehresmann.34 pages, amslatex. The statement in Proposition 3.10 has been correctedQuantum Algebra16W30text