Category Theory Through Functional Programming (part 3/3)
summary
Covers concrete claims and examples: Yoneda lemma isomorphism between natural transformations and K C, the diagonal functor being left adjoint to product with an explicit pair-to-arrow construction, and lists = free monoid as the adjoint to the forgetful functor (fold gives the map back). Shows how unit/counit yield the State return and how right adjoints preserve limits. Uses Haskell/Scala notation and GHC 8 level assumptions, sketches proofs but moves quickly.
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chapters (8)
- 0:00Yoneda Lemma introduction
- 2:32Yoneda Lemma intuition
- 8:24Adjoint functors introduction
- 12:22Adjoint functors example
- 24:59Adjoint functors properties
- 35:20Free and forgetful functors
- 46:07Free monoid as adjoint
- 53:27Summary
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