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Algebraic theories [a categ...
"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"--Provided by publisher
Monografía
monografia Rebiun23551479 https://catalogo.rebiun.org/rebiun/record/Rebiun23551479 m o d cr ||||||||||| 110131s2011 enka sb 001 0 eng d 9780511988646 0511988648 9780511992438 0511992432 9780511760754 0511760752 9780521119221 0521119227 NT eng pn NT YDXCP CDX OSU IUL E7B OCLCQ REDDC OCLCQ DEBSZ OCLCQ AUD OCLCF OCLCQ UAB OCLCQ INT OCLCQ UNAV 512/.62 22 Adámek, Jirí ing Algebraic theories Recurso electrónico] a categorical introduction to general algebra J. Adámek, J. Rosicky, E.M. Vitale ; with a foreword by F .W. Lawvere Cambridge New York Cambridge University Press 2011 Cambridge New York Cambridge New York Cambridge University Press xvii, 249 p. il xvii, 249 p. EBSCO Academic eBook Collection Complete Cambridge tracts in mathematics 184 Incluye referencias bibliográficas e índice Foreword / F.W. Lawvere -- Abstract algebraic categories. Preliminaries -- 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"--Provided by publisher Forma de acceso: World Wide Web Rosicky, Jirí Vitale, E. M.