Monads 1

An introduction to monads including the definition and a look at the monoid monad.

Category:

Howto & Style

Tags:

• category
• functor
• monad
• monoid

[IXISubzeroIXI]

I was pleasantly surprised to find these videos :) I just started learning category theory a few days ago, and while looking up the definition of a homotopy online I saw these videos linked.

Thanks for putting in the effort to make these videos accessible to everyone! As an undergrad, I find it extremely helpful to be able to get a different perspective on categories which doesn't demand mastery of "elementary" math (i.e., algebra) beyond the basics.

[TheCatsters]

Thanks!

[TheCatsters]

Thanks crowlogic and tehrba. I think you each have a point...I've heard that some non-native English speakers were having some trouble so I'll experiment with speaking a little more slowly.  Just a little...

[entropyfails]

A note for Haskell programmers....

η is the mentioned Eta and is the Monadic equivalent of the Haskell "return" function.

μ is the mentioned Mu and is the Monadic equivalent of the "join" operator.

"map" comes for free in Category Theory. So the Haskell bind operator of ">>=" over a list type is x >>= f = join (map f x)

These videos show why the Monad typeclasses must obey the three laws.

1. return a >>= f = f a

2. m >>= return = m

3. (m >>= f) >>= g = m >>= (\x -> f x >>= g)

[chocojian]

YouTube lectures on category theory! Awesome! I hope more mathematicians follow your example in the future. This is a great idea.

[gotgosu]

I really want to watch this but the buzzing in the audio is too offputting. Do you think you can improve the recording?

[targetrich]

phew. Get out, have a drink. read some greek philosophy!

[skip84]

I feel dumb...

[InvisibleScience]

Excellent thanks =]

[mars9050]

Thanks for sharing your teaching skills and math knowledge via the internet. I'm not currently enrolled in an educational institution, so access to lectures is basically impossible for me.

While this isn't a substitute for the ability to pester professors with questions, it's certainly a step in the right direction. Thank you!