2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/33375We extend the calculus of multiplicative vector fields and differential forms and their intrinsic derivatives from Lie groups to Lie groupoids; this generalization turns out to include also the classical process of complete lifting from arbitrary manifolds to tangent and cotangent bundles. Using this calculus we give a new description of the Lie bialgebroid structure associated with a Poisson groupoid.Latex, 27 pages, Quarterly J. Math. (Oxford), to appearDifferential GeometryPrimary 58F05. Secondary 17B66, 22A22, 53C99, 58H05text