Isoclinism of group-groupoids

The relation of being isoclinic between the groups is a weaker equivalence relation than the relation of being isomorphic. That is, groups that are isomorphic are isoclinic, but the reverse is not always true. In recent years, the concept of isoclinism has also been defined for crossed modules over groups. In this thesis, using the equivalence of the category of crossed modules over groups and the category of group-groupoids, the concept of isoclinism between group-groupoids was defined and various properties were examined. This thesis consists of four chapters. In the first chapter, studies in the literature on isoclinism are included. In the second chapter, the concept of isoclinism between groups, the concept of isoclinism between crossed modules on groups and the results obtained in the literature about these concepts are reminded. In the third chapter, the concept of isoclinism between group-groupoids is defined and it is shown that this definition is compatible with the one given in crossed modules over groups. In addition, some important conclusions about the isoclinism of group-groupoids are given. Finally, in the fourth chapter; the results obtained in the thesis are briefly summarized and suggestions for possible future studies on this subject are given.