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Algebraic theories : = a categorical...

Adamek, Jiri, (ing.)

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Algebraic theories : = a categorical introduction to general algebra /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Algebraic theories :/ J. Adamek, J. Rosicky, E.M. Vitale.
Reminder of title:	a categorical introduction to general algebra /
Author:	Adamek, Jiri,
other author:	Rosicky, Jiri.
Published:	New York :Cambridge University Press, : 2011.,
Description:	xvii, 249 p. :ill. ;24 cm.
[NT 15003449]:	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.
Subject:	Categories (Mathematics) -
Online resource:	http://assets.cambridge.org/97805211/19221/cover/9780521119221.jpg
ISBN:	9780521119221 (hardback) :

Algebraic theories : = a categorical introduction to general algebra /
Adamek, Jiri,ing.

Algebraic theories :a categorical introduction to general algebra /J. Adamek, J. Rosicky, E.M. Vitale. - New York :Cambridge University Press,2011. - xvii, 249 p. :ill. ;24 cm. - Cambridge tracts in mathematics ;184.

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"--

ISBN: 9780521119221 (hardback) :US80.00

LCCN: 2010018289Subjects--Topical Terms:

525955
Categories (Mathematics)

LC Class. No.: QA169 / .A31993 2011

Dewey Class. No.: 512/.62

Algebraic theories : = a categorical introduction to general algebra /
LDR:02857cam 22002534a 4500 001 975105
003 DLC
005 20110622114336.0
008 111017s2011 nyua b 001 0 eng
010 $a 2010018289
020 $a 9780521119221 (hardback) : $c US80.00
020 $a 0521119227 (hardback)
035 $a AS-BW-100-N-01
040 $a DLC $c DLC
042 $a pcc
050 0 0 $a QA169 $b .A31993 2011
082 0 0 $a 512/.62 $2 22
100 1 $a Adamek, Jiri, $c ing. $3 884690
245 1 0 $a Algebraic theories : $b a categorical introduction to general algebra / $c J. Adamek, J. Rosicky, E.M. Vitale.
260 # $a New York : $b Cambridge University Press, $c 2011.
300 $a xvii, 249 p. : $b ill. ; $c 24 cm.
490 0 $a Cambridge tracts in mathematics ; $v 184
504 $a Includes bibliographical references and index.
505 8 # $a 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 # $a "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"-- $c Provided by publisher.
650 # 0 $a Categories (Mathematics) $3 525955
650 # 0 $a Algebraic logic. $3 794607
700 1 # $a Rosicky, Jiri. $3 1299004
700 1 # $a Vitale, E. M. $3 1299005
856 4 2 $3 Cover image $u http://assets.cambridge.org/97805211/19221/cover/9780521119221.jpg