Book contents
- Frontmatter
- Dedication
- Contents
- Prologue
- Part One Building up to Categories
- 1 Categories: the idea
- 2 Abstraction
- 3 Patterns
- 4 Context
- 5 Relationships
- 6 Formalism
- 7 Equivalence relations
- 8 Categories: the definition
- Interlude A Tour of Math
- Part Two Doing Category Theory
- Epilogue Thinking categorically
- Appendices
- Glossary
- Further Reading
- Acknowledgements
- Index
5 - Relationships
from Part One - Building up to Categories
Published online by Cambridge University Press: 13 October 2022
- Frontmatter
- Dedication
- Contents
- Prologue
- Part One Building up to Categories
- 1 Categories: the idea
- 2 Abstraction
- 3 Patterns
- 4 Context
- 5 Relationships
- 6 Formalism
- 7 Equivalence relations
- 8 Categories: the definition
- Interlude A Tour of Math
- Part Two Doing Category Theory
- Epilogue Thinking categorically
- Appendices
- Glossary
- Further Reading
- Acknowledgements
- Index
Summary
This chapter introduces the idea of studying things via their relationships with other things. We start with family relationships and the idea of depicting relationships with arrows, and building up relationships by composition. We revisit some of the concepts already discussed, and reframe them as types of relationship. This includes symmetry, basic arithmetic, and modular arithmetic. We look at the relationships between different types of quadrilateral and explore how depicting the relationships with arrows is more powerful than using a Venn diagram. We explore diagrams of factors, fixing a number n and then drawing a lattice of its factors and factor relationships among them. We show that abstracting from this gives us a lattice of subsets of the prime factors of n and that a further abstraction gives us lattices of subsets of any sets. We show that this further abstraction enables us to include a much wider variety of examples, including an analysis of interactions between people with different types of privilege. The idea is to start seeing relationships as something quite general, and to start seeing how abstraction gives us structures that are more widely applicable.
- Type
- Chapter
- Information
- The Joy of AbstractionAn Exploration of Math, Category Theory, and Life, pp. 52 - 66Publisher: Cambridge University PressPrint publication year: 2022