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008 100428s2010 nyu sb 001 0 eng d
050 4 QA169|b.A31993 2010
082 04 512/.62|222
100 1 Adámek, Jiří,|cing.|0http://id.loc.gov/authorities/names/
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.
338 online resource|bcr|2rdacarrier
347 text file|2rdaft|0http://rdaregistry.info/termList/
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)|0http://id.loc.gov/authorities/
650 0 Algebraic logic.|0http://id.loc.gov/authorities/subjects/
655 4 Electronic books.
700 1 Rosický, Jiří.|0http://id.loc.gov/authorities/names/
700 1 Vitale, E. M.|0http://id.loc.gov/authorities/names/
700 1 Lawvere, F. W.|0http://id.loc.gov/authorities/names/
710 2 ProQuest (Firm)|0http://id.loc.gov/authorities/names/
830 0 Cambridge tracts in mathematics ;|0http://id.loc.gov/
856 40 |uhttps://ebookcentral.proquest.com/lib/unimelb/
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