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Algebraic theories: a categorical introduction to general algebra

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Author(s): Adámek, Jiří; Vitale, Enrico M.; Lawvere, Francis W.; Rosický, Jiří
Series: Cambridge tracts in mathematics 184
Edition: Online-ausg.
Publisher: Cambridge University Press
Year: 2011

Language: English
Pages: 249
City: Cambridge
Tags: Algebraic logic.;Categories (Mathematics);Allgemeine Algebra.;Kategorie (Mathematik);Sigma-Algebra.;Algebraic logic

Content: Foreword F. W. Lawvere
Introduction
Preliminaries
Part I. Abstract Algebraic Categories: 1. Algebraic theories and algebraic categories
2. Sifted and filtered colimits
3. Reflexive coequalizers
4. Algebraic categories as free completions
5. Properties of algebras
6. A characterization of algebraic categories
7. From filtered to sifted
8. Canonical theories
9. Algebraic functors
10. Birkhoff's variety theorem
Part II. Concrete Algebraic Categories: 11. One-sorted algebraic categories
12. Algebras for an endofunctor
13. Equational categories of -algebras
14. S-sorted algebraic categories
Part III. Selected Topics: 15. Morita equivalence
16. Free exact categories
17. Exact completion and reflexive-coequalizer completion
18. Finitary localizations of algebraic categories
A. Monads
B. Abelian categories
C. More about dualities for one-sorted algebraic categories
Summary
Bibliography
Index.