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Natural Dualities for the Working Algebraist (Cambridge Studies in Advanced Mathematics)
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.
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
- Bibliography
- Notation index
- Index.
Brief Description:
First text in subject; aimed at algebraists, category theorists in mathematics and computer science.
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