Haskell for Imperative Programmers #36 - Category Theory (Functors, Applicatives, Monads)

In this video we are going to get theoretical!

Programming with categories:

Category theory for programmers by Bartosz Milewski:

Seven Sketches in Compositionality by Brendan Fong & David I. Spivak:

Applicative programming with effect by Conor McBride & Ross Paterson:

Timestamps:
00:00 - Intro
00:24 - Categories
05:13 - Monoids as Categories
06:18 - Functors
09:45 - Monoidal Categories
13:00 - Monoidal Functors
16:39 - Applicatives
19:45 - Monoids
21:04 - Monads
26:23 - Recap
27:42 - Laws
28:01 - Conclusion
28:39 - Recommendations for further study

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[SorokinAnton]

9:20 maybe map f . map g, not map f (map g)

[tatechin]

I've been following your tutorial for like a week now. Probably one of the best tutorials for haskell. Thank you so much!

[AlexandreCassagne]

Your tutorials are fantastic. Thank you for releasing them, they are a rare mix of theory and application that distils the essence of things. More YouTube channels should embrace this method instead of duplicating concepts unnecessarily (as in the ‘tutorial’ culture).

[battatia]

Really liking this series and getting a lot out of it. This is the first where its started to go over my head. Will check out recommended resources and give it another go. Thank you for all of your Haskell content!

[mamo]

Your videos are truly great. This is the first one I didn't quite understand. I'll have to try to rewatch it and read the linked resources.

As a request, are you planning to talk about the State monad or the Arrow class in the future?

Thank you so much for your great videos, keep it up!

[AlessandroZir]

marvelous, I loved those schemes in the beginning!! ❤❤🦊

[VuVietran]

At 18:55, is this a bit misleading because putStrLn <$> getLine is of type IO (IO ()) which doesn't really do anything unless you "join" the IO? To print, surely you need getLine >>= putStrLn?
Many thanks for your vids btw!

[vicissitude]

Can I download these slides from somewhere?

[Fanaro]

How do you create your slides? With LaTeX? If you make it with code, could you please share them as well?

[torsten_dev]

21:10
So a monad is just a monoid in the category of endofunctors?

[hotdog]

At 10:00, you say that the tensor product is a functor, but maps objects of C. My understanding is that would be a morphism, not a functor? Or am I misunderstanding

[ambatimeghana]

Your tutorial awesome.
Can you suggest reference books related to this topic.

[Bratjuuc]

What does "muT" mean? Mu is a natural transformation, while T is a functor. Does this T in muT mean id_T ?

[saltrocklamp]

Sorry to double comment. Are there sensible English pronunciations for $, <$>, <*>, **, and <**>?

[nincako]

this video is NOT about application. The codes given are just definitions and it is heavily based on describing something very abstract. Please do not waste your time.

[segersbenny]

Bartosz has lectures on category theory YouTube as well, very interesting