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Algebraic theories : a categorical introduction to general algebra
detail
Autor: Jiří Adámek, Jiří Rosický, E. M. Vitale, F. W. Lawvere
Rok: 2010
ISBN: 9780521119221
OKCZID: 110767450
Citace (dle ČSN ISO 690):
ADÁMEK, Jiří, Jiří ROSICKÝ a E. M. VITALE. Algebraic theories: a categorical introduction to general algebra. Autor úvodu F. W. LAWVERE. Cambridge ;, New York: Cambridge University Press, 2011, 249 s. Cambridge tracts in mathematics. Algebraic theo
Části díla
Anotace
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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