In this present work, we present the concept of a crossed module over generalized groups and we call it a "generalized crossed module". We also define a generalized group-groupoid. Furthermore, we show that the category of generalized crossed modules is equivalent to that of generalized group-groupoids whose object sets are abelian generalized group.
C1 [Gursoy, Mustafa Habil; Icen, Ilhan] Inonu Univ, Dept Math, Fac Sci & Art, Malatya, Turkey.
[Aslan, Hatice] Firat Univ, Dept Math, Fac Sci, Elazig, Turkey.