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Author:   Jiří Adámek (Czech Technical University in Prague) ,  Stefan Milius (Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany) ,  Lawrence S. Moss (Indiana University, Bloomington)
Publisher:   Cambridge University Press
Imprint:   Cambridge University Press
Dimensions:   Width: 15.20cm , Height: 3.50cm , Length: 22.90cm
Weight:   1.136kg
ISBN:  

9781108835466

ISBN 10:   1108835465
Pages:   640
Publication Date:   06 February 2025
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Manufactured on demand  
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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.

Reviews

'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 König, Universität Duisburg-Essen 'Fixed points are central to computer science. The book is therefore a must for every categorically minded computer scientist.' Ichiro Hasuo, National Institute of Informatics

Author Information

Jiří 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. Stefan Milius is Professor in the Department of Computer Science at Friedrich-Alexander-Universität Erlangen-Nürnberg. An expert in the theory of coalgebras, he is also well known for his work on the category-theoretic approach to the semantics of iteration and recursion, for which he has won the prestigious Ackermann Award. He is one of the inventors of the categorical approach to algebraic language theory. Lawrence S. Moss is Professor in the Mathematics Department at Indiana University Bloomington. He is President of the Association for Logic, Language, and Information, and co-authored 'Vicious Circles' (1996) and 'Mathematical Structures in Language' (2016). He is known for work on dynamic epistemic logic, non-well-founded sets and circularity, coalgebra, natural logic, and other areas of logic and mathematics.

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