Physical description 
xvii, 249 pages. 

polychrome rdacc 
Series 
Cambridge tracts in mathematics ; v. 184. 

Cambridge tracts in mathematics ; 184.

Bibliography 
Includes bibliographical references and index. 
Contents 
Machine generated contents note: 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 [SIGMA]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. 
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" Provided by publisher. 
Reproduction 
Electronic reproduction. Ann Arbor, MI : ProQuest, 2015. Available via World Wide Web. Access may be limited to ProQuest affiliated libraries. 
Other author 
Rosický, Jiří.


Vitale, E. M.


Lawvere, F. W.


ProQuest (Firm)

Subject 
Categories (Mathematics)


Algebraic logic.


Electronic books. 
ISBN 
9780521119221 hardback 

9780511988646 ebook 
