Semigroups in Complete Lattices

Quantales, Modules and Related Topics

  • Patrik Eklund
  • Javier Gutiérrez García
  • Ulrich Höhle
  • Jari Kortelainen

Part of the Developments in Mathematics book series (DEVM, volume 54)

Table of contents

  1. Front Matter
    Pages i-xxi
  2. Patrik Eklund, Javier Gutiérrez García, Ulrich Höhle, Jari Kortelainen
    Pages 1-43
  3. Patrik Eklund, Javier Gutiérrez García, Ulrich Höhle, Jari Kortelainen
    Pages 45-202
  4. Patrik Eklund, Javier Gutiérrez García, Ulrich Höhle, Jari Kortelainen
    Pages 203-288
  5. Back Matter
    Pages 289-326

About this book


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.


MSC (2010) 06F07, 18C20, 18D15, 46L05 quantales and monoidal categories semi-unital quantales balanced and bisymmetric quantales tensor product of quantales spectrum of non-commutative C*-algebras Frobenius quantales and complete MV-algebras modules on unital quantales quantales and enriched category theory automata and free unital quantales

Authors and affiliations

  • Patrik Eklund
    • 1
  • Javier Gutiérrez García
    • 2
  • Ulrich Höhle
    • 3
  • Jari Kortelainen
    • 4
  1. 1.Department of Computing ScienceUmeå UniversityUmeåSweden
  2. 2.Department of MathematicsUniversity of the Basque Country UPV/EHUBilbaoSpain
  3. 3.School of Mathematics and Natural SciencesUniversity of WuppertalWuppertalGermany
  4. 4.Department of Information TechnologySouth-Eastern Finland University of Applied SciencesMikkeliFinland

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-78947-7
  • Online ISBN 978-3-319-78948-4
  • Series Print ISSN 1389-2177
  • Series Online ISSN 2197-795X
  • Buy this book on publisher's site