Gursoy, Mustafa Habil2024-08-042024-08-0420211223-69342246-9958https://hdl.handle.net/11616/100543In this paper, we define the topological versions of the concepts of crossed module over generalized groups, which is called generalized crossed module, and generalized group-groupoid. We construct the categories of the topological generalized crossed modules and their homomorphisms and of the topological generalized group-groupoid and homomorphisms between them. We also obtain some characterizations related to the concepts of topological generalized crossed module and topological generalized group-groupoid. Finally, at the end of the work, we prove that the category of topological generalized crossed modules is equivalent to that of topological generalized group-groupoids whose object sets are commutative topological generalized groups.eninfo:eu-repo/semantics/closedAccessTopological grouptopological generalized groupgeneralized actioncrossed modulegeneralized crossed modulegeneralized group-groupoidArticle4821831932-s2.0-85126653718Q3WOS:000738363600001N/A