J. Adamek, J. Rosicky, E. M. Vitale

Algebraic Theories

A Categorical Introduction to General Algebra

• Gebundenes Buch

Produktbeschreibung

Up-to-date categorical view of sets with extra algebraic structure (data types), with applications in mathematics and theoretical computer science.

Produktdetails

• Verlag: Cambridge University Press
• Seitenzahl: 268
• Erscheinungstermin: 1. April 2011
• Englisch
• Abmessung: 235mm x 157mm x 20mm
• Gewicht: 590g
• ISBN-13: 9780521119221
• ISBN-10: 0521119227
• Artikelnr.: 30364498

Autorenporträt

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.