Some Researches On Universal Arrow Categories

The concept of a universal arrow was initiated by Samuel in1948in connection with his investigations of free topological groups This notion bears enormous generality and strength, and at present it is an essential ingredient of a metamath-ematical viewpoint of mathematic.Many mathematical constructions can be in-terpreted as universal arrow.In the preface,we give a brief introduction of the background related to this dis-sertation, and make a systemic exposition of main results. The dissertation concen-trates on preservability of universal arrow category and construction of Recollement, which includes four chapters altogether.In the first chapter, we study the basic properties of universal arrow. We take the advantage of these properties to discuss the problem of preservation of universal arrow category under abelian category and triangulated category.In the second chapter, we construct a new Recollement of universal arrow cat-egories in the case of the given three abelian categories(triangulated categories) and comparison functors.In the third chapter, we investigate the relationship between universal arrow and universal element. On this basis, we discuss the relationship between universal element category and functor category. Then we give examples of universal element and construct a new Dedekind lattice.In the forth chapter, we sum up the main results of this dissertation.