Crossed modules over grupoids and cat1-grupoids

This thesis consists of four chapter. In the first chapter some fundamental notions such as actions of groups and of groupoids, category, grupoid, crossed modules over groupoids and cat1-group were given. Moreover the proof of the natural equivalence between cat1-groups and crossed modules over groups was given. In the second chapter the fundamental notions of cat1-groupoids was given and the natural equivalence between the category of cat1-groupoids and the category of crossed modules over groupoids was shown. In the third chapter, we defined coverings and actions of cat1-groupoids using underlying groupoids and proved natural equivalence between their categories. Next, the quotient structure of cat1-groupoids was obtained as an original study. In the fourth chapter, suggestions for further works and some results were given.