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    Topological Group-Groupoids and Equivalent Categories
    (2022) Özcan, Abdullah Fatih; İçen, İlhan
    The concept of groupoid was offered by Brandt (1926). The structure of the topological groupoid was given by Ehresmann (1958). A groupoid action is a significant appliance in algebraic topology offered by Ehresmann. Another algebraic notion is a covering given by Brown (1988). The topological group-groupoids (?-groupoid) were first put forward by Icen & Ozcan (2001). The definition of coverings of topological ? groupoid and actions of topological ?-groupoid were also presented by Icen et al. (2005). In this paper, we are going to create a category T?GpdCov(?) of covering morphisms of T?-groupoid and a category T?GpdOp(?) of actions of T?-groupoid. We will then prove that these categories are equivalent.