2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59908A groupoid is a small category in which each morphism has an inverse. A topological groupoid is a groupoid in which both sets of objects and morphisms have topologies such that all groupoid structure maps are continuous. The notion of monodromy groupoid of a topological groupoid generalises those of fundamental groupoid and universal covering. It was earlier proved that the monodromy of a locally sectionable topological groupoid has a topological groupoid structure satisfying some properties. In this paper a similar problem is studied for compatible locally trivial topological groupoids.9 pages, A4Differential GeometryCategory Theory22A05, 55M99, 55R15text