Unique Path Lifting from Homotopy Point of View
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The paper introduces some notions extending the unique path lifting property from a homotopy viewpoint and studies their roles in the category of fibrations. First, we define some homotopical kinds of the unique path lifting property and find all possible relationships between them. Moreover, we supplement the full relationships of these new notions in the presence of fibrations. Second, we deduce some results in the category of fibrations with these notions instead of unique path lifting such as the existence of products and coproducts. Also, we give a brief comparison of these new categories to some categories of the other generalizations of covering maps. Finally, we present two subgroups of the fundamental group related to the fibrations with these notions and compare them to the subgroups of the fundamental group related to covering and generalized covering maps.
KeywordsHomotopically lifting Unique path lifting Fibration Fundamental group Covering map
Mathematics Subject Classification (2010)55P05 57M10 57M05
The authors thank the referee for his/her careful reading and useful suggestions. This research was supported by a grant from Ferdowsi University of Mashhad-Graduate Studies (No. 31685).
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