TY - BOOK ID - 67013416 TI - Algebraic theories AU - Adámek, Jiří AU - Rosický, Jiří AU - Vitale, E M AU - Lawvere, F W PY - 2011 VL - 184 SN - 9780521119221 9780511760754 9780511988646 0511988648 9780511992438 0511992432 0511760752 0521119227 110721307X 1282966979 9786612966972 0511991444 0511990456 051198684X PB - Cambridge Cambridge University Press DB - UniCat KW - Categories (Mathematics) KW - Algebraic logic KW - Algebraic logic. KW - Logic, Symbolic and mathematical KW - Category theory (Mathematics) KW - Algebra, Homological KW - Algebra, Universal KW - Group theory KW - Topology KW - Functor theory UR - https://www.unicat.be/uniCat?func=search&query=sysid:67013416 AB - "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"-- ER -