Category Theory Through Functional Programming (part 2/3)

on YouTube ↗56m

" summary

Explains concrete equivalences and code-level shapes: the category of endofunctors is monoidal under composition with Identity as unit, monads are monoid objects in End(C) and translate to Haskell as join :: m (m a) -> m a and return :: a -> m a, naturality follows from parametricity, and monoidal functors = applicative functors so applicative operations implement the monoidal structure. Shows examples (List, Maybe, Either, Identity, Void), uses Haskell types and polymorphic functions, and notes composed monads fail to be monads unless a distributive law exists.

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" chapters (8)

1. 0:00Introduction to monads
2. 1:03Natural transformations
3. 7:14Monoid objects
4. 15:45Monoidal categories
5. 24:51Monoidal functors
6. 35:27Category of endofunctors
7. 42:22Defining monads
8. 53:32Comonads and conclusions

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