Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- 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
- Appendix A Functors with Initial Algebras or Terminal Coalgebras
- Appendix B A Primer on Fixed Points in Ordered and Metric Structures
- Appendix C Set Functors
- References
- List of Categories
- Index
Appendix B - A Primer on Fixed Points in Ordered and Metric Structures
Published online by Cambridge University Press: 30 January 2025
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- 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
- Appendix A Functors with Initial Algebras or Terminal Coalgebras
- Appendix B A Primer on Fixed Points in Ordered and Metric Structures
- Appendix C Set Functors
- References
- List of Categories
- Index
Summary
This appendix summarizes all of the known fixed point theorems used in the book. In addition to the best known results of this type, it also contains Markowsky’s characterization of directed-complete partial orders, Iwamura’s Lemma, and Pataraia’s ordinal-free version of Zermelo’s Theorem (see Chapter 6). It also mentions induction principles related to these fixed point theorems.
- Type
- Chapter
- Information
- Initial Algebras and Terminal CoalgebrasThe Theory of Fixed Points of Functors, pp. 541 - 551Publisher: Cambridge University PressPrint publication year: 2025