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.
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.
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.
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.
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