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...
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Weitere beteiligte Personen: | , , |
| Format: | E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2011
|
| Schriftenreihe: | Cambridge tracts in mathematics
184 |
| Links: | https://doi.org/10.1017/CBO9780511760754 |
| 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. |
| Umfang: | 1 Online-Ressource (xvii, 249 Seiten) |
| ISBN: | 9780511760754 |
Internformat
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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 |
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 2011 | |
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| 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. | ||
| 700 | 1 | |a Lawvere, F .W. | |
| 700 | 1 | |a Rosický, Jiří | |
| 700 | 1 | |a Vitale, E. M. | |
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| spelling | Adámek, Jiří 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 c cr 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. Lawvere, F .W. Rosický, Jiří Vitale, E. M. Erscheint auch als Druck-Ausgabe 9780521119221 |
| spellingShingle | Adámek, Jiří Algebraic theories a categorical introduction to general algebra |
| 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 |
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