This project will investigate the theory of quantales and their applications. It will utilize lattice theoretic and category theoretic methods to explore the general theory of these partially ordered algebraic structures. The principal investigator will also consider applications to diverse areas such as ring and monoid theory, C*-algebras, and linear logic and its use in theoretical computer science. The research in this project involves category theory and its applications to problems in theoretical computer science. Traditionally, category theory has dealt with the foundations of algebra; namely, it has focused on sets with algebraic structure, mappings between sets that preserve that structure, and even more abstract functors that relate the collections of algebraic structures and their mappings. In recent years, this research subject has enjoyed a rebirth in theoretical computer science.
