This monograph provides a modern introduction to the theory of quantales.
First coined by C.J. Mulvey in 1986, quantales have since developed into a significant topic at the crossroads of algebra and logic, of notable interest to theoretical computer science. This book recasts the subject within the powerful framework of categorical algebra, showcasing its versatility through applications to C*- and MV-algebras, fuzzy sets and automata. With exercises and historical remarks at the end of each chapter, this self-contained book provides readers with a valuable source of references and hints for future research.
This book will appeal to researchers across mathematics and computer science with an interest in category theory, lattice theory, and many-valued logic.
Introduction.- 1 Foundations.- 2 Fundamentals of Quantales.- 3 Module Theory in Sup.- Appendix.- References.- Index.
Patrik Eklund develops applications based on many-valued representation of information. Information typically resides in the form of expressions and terms as integrated in knowledge structures, so that term functors, extendable to monads, become important instrumentations in applications. Categorical term constructions with applications to Goguen's category have been recently achieved (cf. Fuzzy Sets and Syst. 298, 128-157 (2016)). Information representation supported by such monads, and as constructed over monoidal closed categories, inherits many-valuedness in suitable ways also in implementations. "This monograph is a detailed and extensive investigation of the theory of quantales in different areas of mathematics. ... the book is self-contained, well-organized and well-written and is warmly recommended to read." (Ali Madanshekaf, zbMATH 1491.06001, 2022)
