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Sat Jul 21 21:46:32 EDT 2018

## Binary Kleisli Arrow?

I'm still trying to make sense of this, so is this nonsense?
Basically, Categories and monoids are linked through the Hom-set
https://bartoszmilewski.com/2014/12/05/categories-great-and-small/
https://en.wikipedia.org/wiki/Hom_functor
So a monoid is represented such that monoidal composition is function
comosition. For monads this is the similar, but the composition is
Kleisli composition.
So "binary kleisli" makes sense only as Kleisli composition.
So what is a -> b -> m c ?
It's really just (a, b) -> m c
So I guess the questions becomes, "how do you get to m (a,b)" ?
A way to construct a program from linear Kleisli arrow composition, is
to use tuple-shuffling operators.
Note that monads can do something much more powerful, e.g. ANF: how
binding works in do notation. But is that just equivalent to tuple
chaining?

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