BM Category Theory 10.1: Monads

Math Online Tom Circle

10.1Monads

$latex begin{array}{|l|l|l|}
hline
Analogy & Compose & Identity
hline
Function & : : : : “.” & : : : : Id
hline
Monad & ” >> = ” (bind) & return :: “eta”
hline
end{array}$

Imperative (with side effects eg. state, I/O, exception ) to Pure function by hiding or embellishment in Pure function but return “embellished” result.

Monad = functor T + 2 natural transformations

$latex boxed {text {Monad} = {T , eta , mu} }&fg=aa0000&s=3$

$latex eta :: Id dotto T$
$latex mu :: T^{2} dotto T$
$latex text {Natural Transformation : } dotto $

http://adit.io/posts/2013-04-17-functors,_applicatives,_and_monads_in_pictures.html#functors

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