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Algebraic Theories - A Categorical Introduction to General Algebra (Hardcover)
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Algebraic Theories - A Categorical Introduction to General Algebra (Hardcover)
Series: Cambridge Tracts in Mathematics
Expected to ship within 12 - 17 working days
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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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