Product details:
| ISBN13: | 9781108835466 |
| ISBN10: | 1108835465 |
| Binding: | Hardback |
| No. of pages: | 640 pages |
| Size: | 235x159x38 mm |
| Weight: | 1060 g |
| Language: | English |
| 694 |
Category:
Initial Algebras and Terminal Coalgebras
The Theory of Fixed Points of Functors
Publisher: Cambridge University Press
Date of Publication: 6 February 2025
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Publisher's listprice:
GBP 155.00
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Short description:
An in-depth treatment of an active research area of theoretical computer science, presenting and extending its most important results.
Long description:
Providing an in-depth treatment of an exciting research area, this text's central topics are initial algebras and terminal coalgebras, primary objects of study in all areas of theoretical computer science connected to semantics. It contains a thorough presentation of iterative constructions, giving both classical and new results on terminal coalgebras obtained by limits of canonical chains, and initial algebras obtained by colimits. These constructions are also developed in enriched settings, especially those enriched over complete partial orders and complete metric spaces, connecting the book to topics like domain theory. Also included are an extensive treatment of set functors, and the first book-length presentation of the rational fixed point of a functor, and of lifting results which connect fixed points of set functors with fixed points of endofunctors on other categories. Representing more than fifteen years of work, this will be the leading text on the subject for years to come.
'The ultimate book explaining the state-of-the-art in the field of initial algebras and terminal coalgebras. Highly recommended to readers seeking both an introduction as well as an in-depth treatment of a general theory of iteration, with applications in algebraic specification, state-based modelling and behavioural equivalence.' Barbara K&&&246;nig, Universit&&&228;t Duisburg-Essen
'The ultimate book explaining the state-of-the-art in the field of initial algebras and terminal coalgebras. Highly recommended to readers seeking both an introduction as well as an in-depth treatment of a general theory of iteration, with applications in algebraic specification, state-based modelling and behavioural equivalence.' Barbara K&&&246;nig, Universit&&&228;t Duisburg-Essen
Table of Contents:
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.
