Özcan, Abdullah Fatihİçen, İlhan2024-08-042024-08-0420221300-54132667-467Xhttps://doi.org/10.53433/yyufbed.1137668https://search.trdizin.gov.tr/yayin/detay/1146444https://hdl.handle.net/11616/90169The 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.eninfo:eu-repo/semantics/openAccessArticle27366767310.53433/yyufbed.11376681146444