2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/153651We introduce a category of noncommutative bundles. To establish geometry in this category we construct suitable noncommutative differential calculi on these bundles and study their basic properties. Furthermore we define the notion of a connection with respect to a differential calculus and consider questions of existence and uniqueness. At the end these constructions are applied to basic examples of noncommutative bundles over a coquasitriangular Hopf algebra.LaTeX, 31 pagesQuantum Algebra16S40, 16W30,81R50text