Giraldo, A.Rodríguez Sanjurjo, José Manuel2023-06-202023-06-2020011572-914110.1023/A:1013793418931https://hdl.handle.net/20.500.14352/57655In this paper we introduce a class of maps possessing a multivalued homotopy lifting property with respect to every topological space. We call these maps multifibrations and they represent a formally stronger concept than that of shape fibration. Multifibrations have the interesting property of being characterized in a completely intrinsic. way by a path lifting property involving only the total and the base space of the fibration. We also show that multifibrations land also, with some restrictions, shape fibrations) have a lifting property for homotopies of fine multivalued maps. This implies, when the spaces considered are metric compacta, that the possibility of lifting a fine multivalued map is a property of the corresponding strong shape morphism and not of the particular map considered.engjournal articlehttp://www.springerlink.com/content/ur58kq2855685173/fulltext.pdfhttp://www.springerlink.com/open access514515.1shape fibrationmultivalued mappath liftingp ropertystrong shapeGeometríaTopología1204 Geometría1210 Topología