2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59514We show the equivalence of two kinds of strict multiple category, namely the well known globular omega-categories, and the cubical omega-categories with connections.Latex2E, xy, 38 pages. New version 17 Dec 2001, as accepted by Advances in Mathematics: minor but useful corrections. Some pictures addedCategory TheoryAlgebraic Topology18D35, 55U99text