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Algebraic theories : a cate...
"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"--
Monografía
monografia Rebiun36037826 https://catalogo.rebiun.org/rebiun/record/Rebiun36037826 m o d | cr|||||||||||| 100428s2010 nyu ob 001 0 eng d 1-107-21307-X 1-282-96697-9 9786612966972 0-511-99144-4 0-511-99045-6 0-511-99243-2 0-511-98864-8 0-511-76075-2 0-511-98684-X UPVA 998449954803706 UAM 991008020992604211 CBUC 991010754783006709 MiAaPQ eng rda pn MiAaPQ MiAaPQ eng 512/.62 22 Adamek, Jiri ing Algebraic theories a categorical introduction to general algebra J. Adamek, J. Rosicky, E. M. Vitale ; with a foreword by F. W. Lawvere New York Cambridge University Press 2010 New York New York Cambridge University Press 1 online resource (xvii, 249 pages) digital, PDF file(s) 1 online resource (xvii, 249 pages) Text txt rdacontent computer c rdamedia online resource cr rdacarrier Cambridge tracts in mathematics v. 184 Title from publisher's bibliographic system (viewed on 05 Oct 2015) Includes bibliographical references and index 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. One-sorted algebraic categories; 12. Algebras for an endofunctor; 13. Equational categories of [SIGMA]-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, 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"-- Provided by publisher English Categories (Mathematics) Algebraic logic Rosicky, Jiri Vitale, E. M. Lawvere, F. W. 0-521-11922-7 Cambridge tracts in mathematics 184