Possible relationships between whiskered categories and crossed modules

This thesis consists of 4 chapters. In the first chapter, we give basic information about the subject of the thesis. In second chapter, we give some examples of whiskered groupoid using the close relationship between crossed modules and regular groupoids. Also in this chapter , we give the connection between the categories of crossed modules and whiskered groupoids defined by Brown. In this connection, we prove that these categories are not equivalant. The third chapter we define the notion of whiskering operation on categorical commutative algebras and we investige the close relations among the category of whiskered 2- algebras and the category of crossed modules over algebras. In the last section, the results obtained are given and suggestions are made for individuals who want to work on this subject in the future.