Jiri Adamek, Lawrence S. Moss, Stefan Milius

Initial Algebras and Terminal Coalgebras

The Theory of Fixed Points of Functors

• Gebundenes Buch

Produktbeschreibung

This definitive treatment of results in category theory and theoretical computer science covers classical material from new viewpoints and develops a wealth of new topics. The centrepiece is a collection of existence theorems for initial algebras and terminal coalgebras. It will be the standard reference for years to come.

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Produktdetails

• Verlag: Cambridge University Press
• Seitenzahl: 640
• Erscheinungstermin: 6. Februar 2025
• Englisch
• ISBN-13: 9781108835466
• ISBN-10: 1108835465
• Artikelnr.: 70291373

Autorenporträt

Ji¿í Adámek is Professor in the Department of Mathematics at Czech Technical University Prague and Professor Emeritus in the Department of Computer Science at Technical University Braunschweig. He has authored and co-authored ten books, including 'Locally Presentable and Accessible Categories' (1994), 'Abstract and Concrete Categories' (1990), and 'Algebraic Theories' (2011). He is an EATCS Fellow.

Inhaltsangabe

1. Introduction
2. Algebras and coalgebras
3. Finitary iteration
4. Finitary set functors
5. Finitary iteration in enriched settings
6. Transfinite iteration
7. Terminal coalgebras as algebras, initial algebras as coalgebras
8. Well-founded coalgebras
9. State minimality and well-pointed coalgebras
10. Fixed points determined by finite behaviour
11. Sufficient conditions for initial algebras and terminal coalgebras
12. Liftings and extensions from Set
13. Interaction between initial algebras and terminal coalgebras
14. Derived functors
15. Special topics
A. Functors with initial algebras or terminal coalgebras
B. A primer on fixed points in ordered and metric structures
C. Set functors
References
Index of categories
Subject index.