Category Theory as a Tool for Thought
summary
Argues that category theory gives concrete exploration tools: uses duality to flip diagrams and discover sum types, uses universal constructions (cones and limits) to derive the free monoid as List A, builds a comma category to expose initial objects, and shows the classic equivalence monad = monoid in End by changing tensor to composition. Demonstrates practical fallout: foldMap emerges for lists and generalizes to foldFree / unfoldFree for free monads, showing the constructions are mechanical and library-ready.
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chapters (7)
- 0:00Introduction to category theory
- 4:39Core categorical definitions
- 7:54Duality and universal concepts
- 13:42Universal constructions
- 21:33Monoids and comma categories
- 34:50Generalizing to monads
- 41:56Conclusion and summary
