2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60289Bialgebroids, separable bialgebroids, and weak Hopf algebras are compared from a categorical point of view. Then properties of weak Hopf algebras and their applications to finite index and finite depth inclusions of von Neumann algebras are shortly reviewed. A hint is given at a duality between bialgebroid actions and abstract inclusions in 2-categories.AMS-LaTeX, 15 ppQuantum Algebratext