A Crash Course in Category Theory

on YouTube ↗01h 15m

" summary

Starts from concrete type constructions—void, unit, product, sum, List/Option/Either—and shows how they arise from categorical universal properties; models functors as Scala/Haskell type constructors and fmap, natural transformations as polymorphic functions, and explains currying as an adjunction (product ≃ exponent). Claims programming lives in a Cartesian closed category, uses denotational/semantic framing, and culminates in the Yoneda lemma / Yoneda embedding: an object is determined by its incoming arrows.

AI-written summary · about

" chapters (14)

1. 0:00Intro
2. 1:10Why Categories?
3. 2:08Paradox of Programming
4. 12:23Semantics
5. 14:00Functional Programming
6. 22:31Void
7. 30:24Unit
8. 38:08Product Types
9. 39:17Sum (Coproduct)
10. 41:13Sum Types
11. 41:53Monoidal Category
12. 45:34Algebra of Types
13. 50:40Functor
14. 57:29Adjunction

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