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Natural Dualities for the Working Algebraist

Natural Dualities for the Working Algebraist

Part of Cambridge Studies in Advanced Mathematics

  • Date Published: November 1998
  • availability: Available
  • format: Hardback
  • isbn: 9780521454155


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About the Authors
  • The theory of natural dualities, as presented in this text, is broad enough to encompass many known dualities through a rich assortment of substantive theorems, yet concrete enough to be used to generate an array of previously undiscovered dualities. This text will serve as a user manual for algebraists, for category theorists and for those who use algebra in their work, particularly mathematicians and computer scientists interested in non-classical logics. It will also give the specialist a complete account of the foundations, leading to the research frontier of this rapidly developing field. As the first text devoted to the theory of Natural Dualities, it provides an efficient path through a large body of results, examples and applications in this subject which is otherwise available only in scattered research papers. To enable the book to be used in courses, each chapter ends with an extensive exercise set. Several fundamental unsolved problems are included.

    • Was the first book on Natural Dualities
    • Can be used as a reference or as a text; has exercises, examples, and unsolved problems
    • Davey's other book is well-known and widely used
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    Reviews & endorsements

    'One of the aims of the theory of natural dualities is to provide a systematic framework for making algebraic abstractions concrete. This book, written for those working in algebra, whether in the classical vein or with an eye towards applications to other parts of mathematics and to computer science, is the first thorough exposition of duality theory. Here you will find a clear, engaging, and accessible account of all its fundamental methods and key examples, as well as detailed and well-motivated discussions of intriguing and significant open problems. This well written book will be a valuable resource for algebraists, and an invaluable resource for those determined to advance the current flowering of duality theory itself.' George McNulty, University of South Carolina

    'The best is self-contained and well written … contains a wealth of materials …' Zentralblatt

    '… it is written in a readable clear style and can be recommended to researchers and to students of advanced courses.' European Mathematical Society

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    Product details

    • Date Published: November 1998
    • format: Hardback
    • isbn: 9780521454155
    • length: 370 pages
    • dimensions: 229 x 152 x 24 mm
    • weight: 0.71kg
    • contains: 15 b/w illus.
    • availability: Available
  • Table of Contents

    1. Dual adjunctions and where to find them
    2. Natural dualities
    3. Strong dualities
    4. Examples of strong dualities
    5. Sample applications
    6. What makes a duality useful? 7. Piggyback dualities
    8. Optimal dualities and entailment
    9. Completeness theorems for entailment
    10. Dualisable algebras
    Appendix A. Algebras
    Appendix B. Boolean spaces
    Notation index

  • Authors

    David M. Clark, State University of New York, New Paltz

    Brian A. Davey, La Trobe University, Victoria

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