Algebraic Theories
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- Publisher:
- Cambridge University Press
- Publication date:
- 01 June 2011
- 18 November 2010
- ISBN:
- 9780511760754
- 9780521119221
- Dimensions:
- (228 x 152 mm)
- Weight & Pages:
- 0.57kg, 268 Pages
- Dimensions:
- Weight & Pages:
- Series:
- Cambridge Tracts in Mathematics (184)
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- Cambridge Tracts in Mathematics (184)
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Book description
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.
Reviews
'The book is very well written and made as self-contained as it is reasonable for the intended audience of graduate students and researchers.'
Source: Zentralblatt MATH
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