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Mathematician and popular science author Eugenia Cheng is on a mission to show you that mathematics can be flexible, creative, and visual. This joyful journey through the world of abstract mathematics into category theory will demystify mathematical thought processes and help you develop your own thinking, with no formal mathematical background needed. The book brings abstract mathematical ideas down to earth using examples of social justice, current events, and everyday life – from privilege to COVID-19 to driving routes. The journey begins with the ideas and workings of abstract mathematics, after which you will gently climb toward more technical material, learning everything needed to understand category theory, and then key concepts in category theory like natural transformations, duality, and even a glimpse of ongoing research in higher-dimensional category theory. For fans of How to Bake Pi, this will help you dig deeper into mathematical concepts and build your mathematical background.
Prologue
Part I. 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:
9. Examples we've already seen, secretly
10. Ordered sets
11. Small mathematical structures
12. Sets and functions
13. Large worlds of mathematical structures
Part II. Doing Category Theory:
14. Isomorphisms
15. Monics and epics
16. Universal properties
17. Duality
18. Products and coproducts
19. Pullbacks and pushouts
20. Functors
21. Categories of categories
22. Natural transformations
23. Yoneda
24. Higher dimensions
25. Epilogue: thinking categorically
Appendices: A. Background on alphabets
B. Background on basic logic
C. Background on set theory
D. Background on topological spaces
Glossary
Further reading
Acknowledgements
Index.
Description
Mathematician and popular science author Eugenia Cheng is on a mission to show you that mathematics can be flexible, creative, and visual. This joyful journey through the world of abstract mathematics into category theory will demystify mathematical thought processes and help you develop your own thinking, with no formal mathematical background needed. The book brings abstract mathematical ideas down to earth using examples of social justice, current events, and everyday life – from privilege to COVID-19 to driving routes. The journey begins with the ideas and workings of abstract mathematics, after which you will gently climb toward more technical material, learning everything needed to understand category theory, and then key concepts in category theory like natural transformations, duality, and even a glimpse of ongoing research in higher-dimensional category theory. For fans of How to Bake Pi, this will help you dig deeper into mathematical concepts and build your mathematical background.
