The study of recursion categories was introduced in [DH] to carry out an algebraic and intrinsic investigation of structures and phenomena which arise in the classical recursion theory. In this paper a recursion categorical arrangement is proposed for some of the concepts of reduction and relativization which are commonplace in studying classical recursive functions and operators. Indeed, this introduction can be done in a natural way, using categorical concepts already defined, without resorting to special structures. In developing the subject outlined one also has the opportunity of discussing the concept of uniform proof in the context of the recursion categories.