Editing Homotopy lifting property (section)

{{Short description|Homotopy theory in algebraic topology}}
In [[mathematics]], in particular in [[homotopy theory]] within [[algebraic topology]], the '''homotopy lifting property''' (also known as an instance of the '''[[right lifting property]]''' or the '''covering homotopy axiom''') is a technical condition on a [[continuous function]] from a [[topological space]] ''E'' to another one, ''B''. It is designed to support the picture of ''E'' "above" ''B'' by allowing a [[homotopy]] taking place in ''B'' to be moved "upstairs" to ''E''.

For example, a [[covering map]] has a property of ''unique'' local lifting of paths to a given sheet; the uniqueness is because the fibers of a covering map are [[discrete space]]s. The homotopy lifting property will hold in many situations, such as the projection in a [[vector bundle]], [[fiber bundle]] or [[fibration]], where there need be no unique way of lifting.