Algebraic Theories A Categorical Introduction to General Algebra pdf


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Algebraic Theories A Categorical Introduction to General Algebra pdf

Algebraic Theories A Categorical Introduction to General Algebra pdf : Pages 268

By E. M. Vitale, J. Adámek, and J. Rosický

The authors prove the duality between algebraic categories and algebraic theories and discuss Morita equivalence between algebraic theories.

Series: Cambridge Tracts in Mathematics 184

Publisher: Cambridge University Press, Year: 2010

ISBN: 0521119227,9780521119221

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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.

(Cambridge Tracts in Mathematics 184) J. Adámek, J. Rosický, E. M. Vitale, F. W. Lawvere – Algebraic Theories_ A Categorical Introduction to General Algebra-Cambridge University Press (2010)

 


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