Description

Book Synopsis
First up-to-date treatment of the categorical view of sets with extra algebraic structure (data types), with applications in analysis, topology and number theory, geometry, and mathematical physics. A stimulating read for graduate students and researchers in category theory, general algebra, theoretical computer science and algebraic topology.

Trade 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

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.

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

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    A Hardback by J. Adámek, J. Rosický, E. M. Vitale

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      Book details

      Publisher Cambridge University Press
      Published 11/18/2010 12:00:00 AM
      ISBN-13 9780521119221
      978-0521119221
      ISBN-10 0521119227
      Also in:
      Algebra Mathematical foundations

      Description

      Book Synopsis
      First up-to-date treatment of the categorical view of sets with extra algebraic structure (data types), with applications in analysis, topology and number theory, geometry, and mathematical physics. A stimulating read for graduate students and researchers in category theory, general algebra, theoretical computer science and algebraic topology.

      Trade 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

      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.

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