Abstract. In this paper we generalize fibrations by H-fibrations, the maps which homotopically lift homotopies. We replace the equalities in the defini- tion of covering homotopy property with the homotopy relation so that we can first get an expression of the concept of covering homotopy property in the homotopy category. After introducing H-fibrations, we will have a ho- motopy expression of some concepts related to fibration, such as path lifting, lifting function and unique path lifting property, to generalize some results in fibration. In particular, we show that an H-fibration has homotopical path lifting property and also prove that a map is an H-fibration if and only if it has a homotopical lifting function.

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