Generalized crossed modules over generalized group-groupoids (Q6569322)

Generalized groups were introduced by \textit{M. R. Molaei} [Bul. Inst. Politeh. Iași, Secț. I, Mat. Mec. Teor. Fiz. 45(49), No. 3--4, 21--24 (1999; Zbl 1002.20038)].\N\N\textit{M. H. Gürsoy} et al. [Turk. J. Math. 41, No. 6, 1535--1551 (2017; Zbl 1424.22003)] defined the concept of generalized group-groupoids and they showed that the category of generalized group-groupoids whose object sets are abelian and the full subcategory of generalized crossed modules of generalized group-groupoids are categorically equivalent.\N\N\N\textit{S. Temel} et al. [Filomat 34, No. 6, 1755--1769 (2020; Zbl 1497.18017)] proved the correspondence between crossed modules over group-groupoids and double group-groupoids.\N\NThe article under review introduces generalized double groupoids. Then the categorical equivalence of crossed modules of generalised group-groupoids and generalised double group-groupoids is proved.