Schreier 2-categories

This thesis consists of four chapter. In the first chapter some fundamental notions such as actions of groups and of monoids, category, internal category, grupoid, crossed module and crossed semimodule were given. In the second chapter the natural equivalence between the category of crossed semimodules over monoids and the category of Schreier internal categories in the category of monoids was shown, and then the definitions of crossed semimodule over categories and of Schreier 2-category were given and the natural transformation between their categories was proved. In the third chapter, some results, in the fourth chapter, some suggestions for further works were given.