Up-to-date categorical view of sets with extra algebraic structure (data types), with applications in mathematics and theoretical computer science.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
J. Adámek is a Professor in the Institute of Theoretical Computer Science at the University of Technology, Braunschweig, Germany.
Inhaltsangabe
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.
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.
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