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Home > Mathematics and Science Textbooks > Mathematics > Algebra > Algebraic Theories: A Categorical Introduction to General Algebra(Series Number 184 Cambridge Tracts in Mathematics)
Algebraic Theories: A Categorical Introduction to General Algebra(Series Number 184 Cambridge Tracts in Mathematics)

Algebraic Theories: A Categorical Introduction to General Algebra(Series Number 184 Cambridge Tracts in Mathematics)


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About the Book

Algebraic theories, introduced as a concept in the 1960s, have been a fundamental step towards a categorical view of general algebra. Moreover, they have proved very useful in various areas of mathematics and computer science. This carefully developed book gives a systematic introduction to algebra based on algebraic theories that is accessible to both graduate students and researchers. It will facilitate interactions of general algebra, category theory and computer science. A central concept is that of sifted colimits - that is, those commuting with finite products in sets. The authors prove the duality between algebraic categories and algebraic theories and discuss Morita equivalence between algebraic theories. They also pay special attention to one-sorted algebraic theories and the corresponding concrete algebraic categories over sets, and to S-sorted algebraic theories, which are important in program semantics. The final chapter is devoted to finitary localizations of algebraic categories, a recent research area.

Table of Contents:
Foreword F. W. Lawvere; Introduction; Preliminaries; Part I. Abstract Algebraic Categories: 1. Algebraic theories and algebraic categories; 2. Sifted and filtered colimits; 3. Reflexive coequalizers; 4. Algebraic categories as free completions; 5. Properties of algebras; 6. A characterization of algebraic categories; 7. From filtered to sifted; 8. Canonical theories; 9. Algebraic functors; 10. Birkhoff's variety theorem; Part II. Concrete Algebraic Categories: 11. One-sorted algebraic categories; 12. Algebras for an endofunctor; 13. Equational categories of Σ-algebras; 14. S-sorted algebraic categories; Part III. Selected Topics: 15. Morita equivalence; 16. Free exact categories; 17. Exact completion and reflexive-coequalizer completion; 18. Finitary localizations of algebraic categories; A. Monads; B. Abelian categories; C. More about dualities for one-sorted algebraic categories; Summary; Bibliography; Index.

About the Author :
J. Adámek is a Professor in the Institute of Theoretical Computer Science at the University of Technology, Braunschweig, Germany. J. Rosický is a Professor in the Department of Mathematics and Statistics at Masaryk University, Brno, Czech Republic. E. M. Vitale is a Professor in the Institut de Recherche en Mathématique et Physique at the Université Catholique de Louvain, Louvain-la-Neuve, Belgium.

Review :
'The book is very well written and made as self-contained as it is reasonable for the intended audience of graduate students and researchers.' Zentralblatt MATH


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Product Details
  • ISBN-13: 9780521119221
  • Publisher: Cambridge University Press
  • Publisher Imprint: Cambridge University Press
  • Height: 231 mm
  • No of Pages: 268
  • Returnable: N
  • Series Title: Series Number 184 Cambridge Tracts in Mathematics
  • Sub Title: A Categorical Introduction to General Algebra
  • Width: 155 mm
  • ISBN-10: 0521119227
  • Publisher Date: 18 Nov 2010
  • Binding: Hardback
  • Language: English
  • Returnable: N
  • Returnable: N
  • Spine Width: 23 mm
  • Weight: 566 gr


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Algebraic Theories: A Categorical Introduction to General Algebra(Series Number 184 Cambridge Tracts in Mathematics)
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