Braided regular 2-grupoids

This thesis consits of 5 chapters. In the first chapter, we give some basic informations to use they in this thesis such as category, crossed modules, functors, semi-direct product of groups, Furthermore, we define a functor from the category of pre-crossed modules to that of crossed modules of groups. We investigate the relations between the concepts of groupoids and crossed modules of groups.In the second chapter, from [11] , we investigate the notion of crossed modules over groupoids. By using a similar construction to İçen [26], we have constructed an equivalence between categorical groupoids and crossed modules of groupoids. Moreover, in this chapter, we gave the equivalence between braided regular crossed modules and 2-crossed modules from [11], to use it in the next sections.In chapter 4, we give the notion of braided regular 2-groupoids from Ulualan [37], and again, from [37] we gave the construction of the equivalence between braided regular 2-groupoids and braided regular crossed modules.Consequently, in the last chapter, by using these results given in the chapter 3 and 4, we gave an equivalence between the category of 2-crossed modules of groups and the category of braided regular 2-groupoids.