Algebraic theories :: a categorical introduction to general algebra /
"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 al...
Gespeichert in:
| 1. Verfasser: | |
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| Weitere Verfasser: | , |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York :
Cambridge University Press,
2011.
|
| Schriftenreihe: | Cambridge tracts in mathematics ;
184. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | "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 |
| Beschreibung: | 1 online resource (xvii, 249 pages) : illustrations |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9780511988646 0511988648 9780511992438 0511992432 9780511760754 0511760752 |
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| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | |a Foreword / F.W. Lawvere -- Abstract algebraic categories. Preliminaries -- Algebraic theories and algebraic categories -- Sifted and filtered colimits -- Reflexive coequalizers -- Algebraic categories as free completions -- Properties of algebras -- A characterization of algebraic categories -- From filtered to sifted -- Canonical theories -- Algebraic functors -- Birkhoff's variety theorem -- Concrete algebraic categories. One-sorted algebraic categories -- Algebras for an endofunctor -- Equational categories of [SIGMA]-algebras -- S-sorted algebraic categories -- Selected topics. Morita equivalence -- Free exact categories -- Exact completion and reflexive-coequalizer completion -- Finitary localizations of algebraic categories. Monads -- Abelian categories -- More about dualities for one-sorted algebraic categories. | |
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| author | Adámek, Jiří, 1947- |
| author2 | Rosický, Jiří Vitale, E. M. |
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| contents | Foreword / F.W. Lawvere -- Abstract algebraic categories. Preliminaries -- Algebraic theories and algebraic categories -- Sifted and filtered colimits -- Reflexive coequalizers -- Algebraic categories as free completions -- Properties of algebras -- A characterization of algebraic categories -- From filtered to sifted -- Canonical theories -- Algebraic functors -- Birkhoff's variety theorem -- Concrete algebraic categories. One-sorted algebraic categories -- Algebras for an endofunctor -- Equational categories of [SIGMA]-algebras -- S-sorted algebraic categories -- Selected topics. Morita equivalence -- Free exact categories -- Exact completion and reflexive-coequalizer completion -- Finitary localizations of algebraic categories. Monads -- Abelian categories -- More about dualities for one-sorted algebraic categories. |
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| dewey-ones | 512 - Algebra |
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| discipline | Mathematik |
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| id | ZDB-4-EBA-ocn699490300 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:17:40Z |
| institution | BVB |
| isbn | 9780511988646 0511988648 9780511992438 0511992432 9780511760754 0511760752 |
| language | English |
| oclc_num | 699490300 |
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| physical | 1 online resource (xvii, 249 pages) : illustrations |
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| series | Cambridge tracts in mathematics ; |
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| spelling | Adámek, Jiří, 1947- https://id.oclc.org/worldcat/entity/E39PBJdh6xCWtDR869wFJThj4q Algebraic theories : a categorical introduction to general algebra / J. Adámek, J. Rosický, E.M. Vitale ; with a foreword by F .W. Lawvere. Cambridge ; New York : Cambridge University Press, 2011. 1 online resource (xvii, 249 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Cambridge tracts in mathematics ; 184 "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 Includes bibliographical references and index. Foreword / F.W. Lawvere -- Abstract algebraic categories. Preliminaries -- Algebraic theories and algebraic categories -- Sifted and filtered colimits -- Reflexive coequalizers -- Algebraic categories as free completions -- Properties of algebras -- A characterization of algebraic categories -- From filtered to sifted -- Canonical theories -- Algebraic functors -- Birkhoff's variety theorem -- Concrete algebraic categories. One-sorted algebraic categories -- Algebras for an endofunctor -- Equational categories of [SIGMA]-algebras -- S-sorted algebraic categories -- Selected topics. Morita equivalence -- Free exact categories -- Exact completion and reflexive-coequalizer completion -- Finitary localizations of algebraic categories. Monads -- Abelian categories -- More about dualities for one-sorted algebraic categories. Print version record. Categories (Mathematics) http://id.loc.gov/authorities/subjects/sh85020992 Algebraic logic. http://id.loc.gov/authorities/subjects/sh85003435 Catégories (Mathématiques) Logique algébrique. Algebraic logic fast Categories (Mathematics) fast Rosický, Jiří. http://id.loc.gov/authorities/names/nr94022119 Vitale, E. M. http://id.loc.gov/authorities/names/n2010026559 has work: Algebraic theories (Text) https://id.oclc.org/worldcat/entity/E39PCGKJcmhRBBrmxh7J69tCw3 https://id.oclc.org/worldcat/ontology/hasWork Print version: Adámek, Jiří, ing. Algebraic theories. Cambridge, UK ; New York : Cambridge University Press, 2011 9780521119221 (DLC) 2010018289 (OCoLC)615339131 Cambridge tracts in mathematics ; 184. http://id.loc.gov/authorities/names/n42005726 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=352502 Volltext |
| spellingShingle | Adámek, Jiří, 1947- Algebraic theories : a categorical introduction to general algebra / Cambridge tracts in mathematics ; Foreword / F.W. Lawvere -- Abstract algebraic categories. Preliminaries -- Algebraic theories and algebraic categories -- Sifted and filtered colimits -- Reflexive coequalizers -- Algebraic categories as free completions -- Properties of algebras -- A characterization of algebraic categories -- From filtered to sifted -- Canonical theories -- Algebraic functors -- Birkhoff's variety theorem -- Concrete algebraic categories. One-sorted algebraic categories -- Algebras for an endofunctor -- Equational categories of [SIGMA]-algebras -- S-sorted algebraic categories -- Selected topics. Morita equivalence -- Free exact categories -- Exact completion and reflexive-coequalizer completion -- Finitary localizations of algebraic categories. Monads -- Abelian categories -- More about dualities for one-sorted algebraic categories. Categories (Mathematics) http://id.loc.gov/authorities/subjects/sh85020992 Algebraic logic. http://id.loc.gov/authorities/subjects/sh85003435 Catégories (Mathématiques) Logique algébrique. Algebraic logic fast Categories (Mathematics) fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85020992 http://id.loc.gov/authorities/subjects/sh85003435 |
| title | Algebraic theories : a categorical introduction to general algebra / |
| title_auth | Algebraic theories : a categorical introduction to general algebra / |
| title_exact_search | Algebraic theories : a categorical introduction to general algebra / |
| title_full | Algebraic theories : a categorical introduction to general algebra / J. Adámek, J. Rosický, E.M. Vitale ; with a foreword by F .W. Lawvere. |
| title_fullStr | Algebraic theories : a categorical introduction to general algebra / J. Adámek, J. Rosický, E.M. Vitale ; with a foreword by F .W. Lawvere. |
| title_full_unstemmed | Algebraic theories : a categorical introduction to general algebra / J. Adámek, J. Rosický, E.M. Vitale ; with a foreword by F .W. Lawvere. |
| title_short | Algebraic theories : |
| title_sort | algebraic theories a categorical introduction to general algebra |
| title_sub | a categorical introduction to general algebra / |
| topic | Categories (Mathematics) http://id.loc.gov/authorities/subjects/sh85020992 Algebraic logic. http://id.loc.gov/authorities/subjects/sh85003435 Catégories (Mathématiques) Logique algébrique. Algebraic logic fast Categories (Mathematics) fast |
| topic_facet | Categories (Mathematics) Algebraic logic. Catégories (Mathématiques) Logique algébrique. Algebraic logic |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=352502 |
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