Initial Algebras and Terminal Coalgebras
eBook - PDF

Initial Algebras and Terminal Coalgebras

The Theory of Fixed Points of Functors

  1. 642 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Initial Algebras and Terminal Coalgebras

The Theory of Fixed Points of Functors

About this book

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.

Trusted by 375,005 students

Access to over 1.5 million titles for a fair monthly price.

Study more efficiently using our study tools.

Information

Publisher
Cambridge University Press
Year
2025
Topic
Computer Science
eBook ISBN
9781108880671
Subtopic
Programming Languages
Index
Computer Science

Table of contents

  1. Cover
  2. Half-title page
  3. Series page
  4. Title page
  5. Copyright page
  6. Dedication
  7. Contents
  8. Preface
  9. 1 Introduction
  10. 2 Algebras and Coalgebras
  11. 3 Finitary Iteration
  12. 4 Finitary Set Functors
  13. 5 Finitary Iteration in Enriched Settings
  14. 6 Transfinite Iteration
  15. 7 Terminal Coalgebras as Algebras, Initial Algebras as Coalgebras
  16. 8 Well-Founded Coalgebras
  17. 9 State Minimality and Well-Pointed Coalgebras
  18. 10 Fixed Points Determined by Finite Behaviour
  19. 11 Sufficient Conditions for Initial Algebras and Terminal Coalgebras
  20. 12 Liftings and Extensions from Set
  21. 13 Interaction between Initial Algebras and Terminal Coalgebras
  22. 14 Derived Functors
  23. 15 Special Topics
  24. Appendix A Functors with Initial Algebras or Terminal Coalgebras
  25. Appendix B A Primer on Fixed Points in Ordered and Metric Structures
  26. Appendix C Set Functors
  27. References
  28. List of Categories
  29. Index

Frequently asked questions

Yes, you can cancel anytime from the Subscription tab in your account settings on the Perlego website. Your subscription will stay active until the end of your current billing period. Learn how to cancel your subscription
No, books cannot be downloaded as external files, such as PDFs, for use outside of Perlego. However, you can download books within the Perlego app for offline reading on mobile or tablet. Learn how to download books offline
Perlego offers two plans: Essential and Complete
  • Essential is ideal for learners and professionals who enjoy exploring a wide range of subjects. Access the Essential Library with 800,000+ trusted titles and best-sellers across business, personal growth, and the humanities. Includes unlimited reading time and Standard Read Aloud voice.
  • Complete: Perfect for advanced learners and researchers needing full, unrestricted access. Unlock 1.5M+ books across hundreds of subjects, including academic and specialized titles. The Complete Plan also includes advanced features like Premium Read Aloud and Research Assistant.
Both plans are available with monthly, semester, or annual billing cycles.
We are an online textbook subscription service, where you can get access to an entire online library for less than the price of a single book per month. With over 1.5 million books across 990+ topics, we’ve got you covered! Learn about our mission
Look out for the read-aloud symbol on your next book to see if you can listen to it. The read-aloud tool reads text aloud for you, highlighting the text as it is being read. You can pause it, speed it up and slow it down. Learn more about Read Aloud
Yes! You can use the Perlego app on both iOS and Android devices to read anytime, anywhere — even offline. Perfect for commutes or when you’re on the go.
Please note we cannot support devices running on iOS 13 and Android 7 or earlier. Learn more about using the app
Yes, you can access Initial Algebras and Terminal Coalgebras by Jiří Adámek,Stefan Milius,Lawrence S. Moss in PDF and/or ePUB format, as well as other popular books in Computer Science & Programming Languages. We have over 1.5 million books available in our catalogue for you to explore.