Algebraic theories : a categorical introduction to general algebra
 Responsibility
 J. Adámek, J. Rosický, E.M. Vitale ; with a foreword by F.W. Lawvere.
 Imprint
 Cambridge, UK ; New York : Cambridge University Press, 2011.
 Physical description
 xvii, 249 p. : ill. ; 24 cm.
 Series
 Cambridge tracts in mathematics 184.
Online
At the library
Science Library (Li and Ma)
Stacks
Call number  Note  Status 

QA169 .A31993 2011  Unknown 
More options
Description
Creators/Contributors
 Author/Creator
 Adámek, Jiří, 1947
 Contributor
 Rosický, Jiří.
 Vitale, E. M.
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 241244) and index.
 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. Onesorted algebraic categories
 12. Algebras for an endofunctor
 13. Equational categories of algebras
 14. Ssorted algebraic categories
 Part III. Selected Topics: 15. Morita equivalence
 16. Free exact categories
 17. Exact completion and reflexivecoequalizer completion
 18. Finitary localizations of algebraic categories
 A. Monads
 B. Abelian categories
 C. More about dualities for onesorted algebraic categories
 Summary
 Bibliography
 Index.
 (source: Nielsen Book Data)
 Publisher's summary

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 onesorted algebraic theories and the corresponding concrete algebraic categories over sets, and to Ssorted algebraic theories, which are important in program semantics. The final chapter is devoted to finitary localizations of algebraic categories, a recent research area.
(source: Nielsen Book Data)
Subjects
 Subjects
 Categories (Mathematics)
 Algebraic logic.
Bibliographic information
 Publication date
 2011
 Series
 Cambridge tracts in mathematics ; 184
 ISBN
 9780521119221 (hardback)
 0521119227 (hardback)