Braided 2-crossed modules

This thesis consists of four chapters. In the first chapter, it is given that the basic concepts as crossed modules, whiskered grupoids as well as some basic information that will be used in the thesis about category theory.In the second chapter, braiding map on 2-crossed modules is defined and after brief prior knowledge is given about the simplicial groups and maps , by using the images of these maps, a functor is constructed in the category of 2-crossed modules from the category of reduced simplicial groups with Moore complex of length . Afterward, by defining the reverse functor , it is obtained an equivalance of the related categories.In the third chapter, some special conditions of braided 2-crossed modules are examined. It is also given in this chapter that the relations among these structures and some known algebraic models.Finally, in the fourth chapter, whiskering maps for R-algebroids are defined and the relationship between these whiskered R-algebroids and crossed modules of commutative algebras is proved. In addition, the braiding map on 2-crossed modules of commutative algebras is defined and its relationship with simplicial algebras is given.