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003    MiAaPQ 
006    m     o  d |       
007    cr cn||||||||| 
008    100428s2010    nyu     sb    001 0 eng d 
010    |z2010018289 
019    EBC647362 
019    ebr10442857 
020    |z9780521119221|qhardback 
020    |z9780511988646|qe-book 
035    (MiAaPQ)EBC647362 
035    (Au-PeEL)EBL647362 
035    (CaPaEBR)ebr10442857 
035    (CaONFJC)MIL296697 
035    (OCoLC)700706147 
035    .b40588063 
040    MiAaPQ|beng|cMiAaPQ|dMiAaPQ 
050  4 QA169|b.A31993 2010 
082 04 512/.62|222 
100 1  Adámek, Jiří,|cing.|0
245 10 Algebraic theories :|ba categorical introduction to 
       general algebra /|cJ. Adámek, J. Rosický, E. M. Vitale ; 
       with a foreword by F. W. Lawvere. 
264  1 New York :|bCambridge University Press,|c2010. 
300    xvii, 249 pages. 
336    text|btxt|2rdacontent 
337    computer|bc|2rdamedia 
338    online resource|bcr|2rdacarrier 
340    |gpolychrome|2rdacc|0
347    text file|2rdaft|0
490 1  Cambridge tracts in mathematics ;|vv. 184. 
504    Includes bibliographical references and index. 
505 8  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. 
520    "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"--|cProvided by publisher. 
533    Electronic reproduction. Ann Arbor, MI : ProQuest, 2015. 
       Available via World Wide Web. Access may be limited to 
       ProQuest affiliated libraries. 
650  0 Categories (Mathematics)|0
650  0 Algebraic logic.|0
655  4 Electronic books. 
700 1  Rosický, Jiří.|0
700 1  Vitale, E. M.|0
700 1  Lawvere, F. W.|0
710 2  ProQuest (Firm)|0
830  0 Cambridge tracts in mathematics ;|0
856 40 |u
       detail.action?docID=647362|zConnect to ebook (University 
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907    .b40588063 
990    MARCIVE MELB 201906 
990    ProQuest EBL purchased 
990    Batch Ebook load (bud2) - do not edit, delete or attach 
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