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    Crossed modules, double group-groupoids and crossed squares
    (University of Nis, 2020) Temel, Sedat; Şahan, Tunçar; Mucuk, Osman
    The purpose of this paper is to obtain the notion of crossed module over group-groupoids con-sidering split extensions and prove a categorical equivalence between these types of crossed modules and double group-groupoids. This equivalence enables us to produce various examples of double groupoids. We also prove that crossed modules over group-groupoids are equivalent to crossed squares.