Category Theory 2

  add(1,1) // 2

You will know exactly what this does.

associative (can group them in any order)
commutative (the arguments can come in any order)
identity (with a 0 argument it returns the the other argument)
distributive (can use it in any other composition/function (with multiply for example)

Then shows that add can use any type of arguments, not just integers (strings, floats, arrays).

You have intuitions and laws behind what add can do and it always holds (does what you think it should do).

talks about compose. The above laws apply to it as well. (Same as add).

Talks about the type signature (b -> c) meaning a function that takes b and returns c. (this is a Haskell type signature)

compose :: (b -> c) -> (a -> b) -> (a -> c)

id :: a -> a

You need a composition and an id function to create a category

The identity function (above, just gives back the same value)

Uses the identity function (id) below

  // left identity
compose(id, f) == f

// rigth identity
compose(f, id) == f

// associativity
compose(compose(f,g), h) == compose(f, compose(g,h))

Demoes on jsbin that since compose is associative, he can group the functions in any way he wants (and extract them). Just like add

Abundancia