Fuzzy Z-Quantale And Quantale Algebra Categories

Mulvey introduced the concept of quantales in 1986 with the purpose of study-ing the spectrum of C*-algebra,in order to provide a lattice-theoretic setting for studying non-commutative C*-algebra,as well as constructive foundations for quan-tum mechanics.Because of the good structures about order,topology and algebra,quantale is of great importance in many fields,such as the C*-algebra,linear logic,and theoretical computer science,etc.Fuzzy Z-quantales and quantale algebras are two important contents of quantale theory which are worth studying.Therefore,this paper studies basic properties and some results about fuzzy Z-quantale structures and the category of quantale algebras.The contents of this paper are as follows:Chapter One Preliminaries.In this chapter,we give some basic concepts and results which will be used in this paper.Chapter Two The reflective subcategory of fuzzy Z-quantales.We use the pre-nuclei of fuzzy quantale to prove that the category of fuzzy quantales is a reflec-tive subcategory of the category of fuzzy Z-quantales.On the basis of this result,we give the concrete fuzzy quantale structure generated by the image of universial mapping.We discuss the fuzzy Galois connection constructed by the reflector.Chapter Three The category of quantale algebras.First,we discuss the re-lated properties of quantale algebras.Second,we consider the relationships between Q-Alg(the category of quantale algebras)and Quant(the category of quantales).We find that Q-Alg is a reflective subcategory of Quant.However,Q-Alg is not usually the coreflective subcategory of Quant.Finally,it is proved that Q-Alg has equalizer and coequalizer.From these properties,we immediately conclude that Q-Alg is an algebraic category.