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 algebra...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
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Cambridge
Cambridge University Press
2011
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| Schriftenreihe: | Cambridge tracts in mathematics
184 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 UBR01 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 |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 Online-Ressource (xvii, 249 Seiten) |
| ISBN: | 9780511760754 |
| DOI: | 10.1017/CBO9780511760754 |
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| 245 | 1 | 0 | |a Algebraic theories |b a categorical introduction to general algebra |c J. Adámek, J. Rosický, E.M. Vitale ; with a foreword by F .W. Lawvere |
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| 500 | |a Title from publisher's bibliographic system (viewed on 05 Oct 2015) | ||
| 505 | 8 | |a Foreword / F.W. Lawvere -- Preliminaries. Abstract Algebraic Categories. 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 | |
| 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 | ||
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| 700 | 1 | |a Rosický, Jiří |d 1946- |e Sonstige |0 (DE-588)136237118 |4 oth | |
| 700 | 1 | |a Vitale, Enrico M. |d 1964- |e Sonstige |0 (DE-588)143009931 |4 oth | |
| 700 | 1 | |a Lawvere, Francis W. |d 1937-2023 |0 (DE-588)108079104 |4 aui | |
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Datensatz im Suchindex
| _version_ | 1804176883520110592 |
|---|---|
| any_adam_object | |
| author | Adámek, Jiří 1947- |
| author2 | Lawvere, Francis W. 1937-2023 |
| author2_role | aui |
| author2_variant | f w l fw fwl |
| author_GND | (DE-588)113295219 (DE-588)136237118 (DE-588)143009931 (DE-588)108079104 |
| author_facet | Adámek, Jiří 1947- Lawvere, Francis W. 1937-2023 |
| author_role | aut |
| author_sort | Adámek, Jiří 1947- |
| author_variant | j a ja |
| building | Verbundindex |
| bvnumber | BV043941573 |
| classification_rvk | SK 230 |
| collection | ZDB-20-CBO |
| contents | Foreword / F.W. Lawvere -- Preliminaries. Abstract Algebraic Categories. 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 |
| ctrlnum | (ZDB-20-CBO)CR9780511760754 (OCoLC)967601153 (DE-599)BVBBV043941573 |
| dewey-full | 512/.62 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.62 |
| dewey-search | 512/.62 |
| dewey-sort | 3512 262 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511760754 |
| format | Electronic eBook |
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| id | DE-604.BV043941573 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9780511760754 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350543 |
| oclc_num | 967601153 |
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| owner | DE-12 DE-92 DE-355 DE-BY-UBR |
| owner_facet | DE-12 DE-92 DE-355 DE-BY-UBR |
| physical | 1 Online-Ressource (xvii, 249 Seiten) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO ZDB-20-CBO UBR Einzelkauf (Lückenergänzung CUP Serien 2018) |
| publishDate | 2011 |
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| publisher | Cambridge University Press |
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| spelling | Adámek, Jiří 1947- Verfasser (DE-588)113295219 aut Algebraic theories a categorical introduction to general algebra J. Adámek, J. Rosický, E.M. Vitale ; with a foreword by F .W. Lawvere Cambridge Cambridge University Press 2011 1 Online-Ressource (xvii, 249 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 184 Title from publisher's bibliographic system (viewed on 05 Oct 2015) Foreword / F.W. Lawvere -- Preliminaries. Abstract Algebraic Categories. 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 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 Categories (Mathematics) Algebraic logic Allgemeine Algebra (DE-588)4567805-4 gnd rswk-swf Sigma-Algebra (DE-588)4181252-9 gnd rswk-swf Kategorie Mathematik (DE-588)4129930-9 gnd rswk-swf Kategorie Mathematik (DE-588)4129930-9 s Allgemeine Algebra (DE-588)4567805-4 s Sigma-Algebra (DE-588)4181252-9 s DE-604 Rosický, Jiří 1946- Sonstige (DE-588)136237118 oth Vitale, Enrico M. 1964- Sonstige (DE-588)143009931 oth Lawvere, Francis W. 1937-2023 (DE-588)108079104 aui Erscheint auch als Druck-Ausgabe 978-0-521-11922-1 https://doi.org/10.1017/CBO9780511760754 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Adámek, Jiří 1947- Algebraic theories a categorical introduction to general algebra Foreword / F.W. Lawvere -- Preliminaries. Abstract Algebraic Categories. 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) Algebraic logic Allgemeine Algebra (DE-588)4567805-4 gnd Sigma-Algebra (DE-588)4181252-9 gnd Kategorie Mathematik (DE-588)4129930-9 gnd |
| subject_GND | (DE-588)4567805-4 (DE-588)4181252-9 (DE-588)4129930-9 |
| 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) Algebraic logic Allgemeine Algebra (DE-588)4567805-4 gnd Sigma-Algebra (DE-588)4181252-9 gnd Kategorie Mathematik (DE-588)4129930-9 gnd |
| topic_facet | Categories (Mathematics) Algebraic logic Allgemeine Algebra Sigma-Algebra Kategorie Mathematik |
| url | https://doi.org/10.1017/CBO9780511760754 |
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