[Haskell-cafe] N and R are categories, no?

[Steve Downey]

EOk, i'm trying to write down, not another monad tutorial, because I
don't know that much yet, but an explication of my current
understanding of monads.

But before I write down something that is just flat worng, I thought
I'd get a cross check. (and I can't get to #haskell)

Monads are Functors. Functors are projections from one category to
another such that structure is preserved. One example I have in mind
is the embedding of the natural numbers into the real numbers. The
mapping is so good, that we don't flinch at saying 1 == 1.0.

The functor that takes us from N to R is probably a Monad, that is, if
N and R are categories.

The real hard part is tying together how unit, join and bind produce a
spacesuit that can protect apples from nuclear waste. I'm still
getting that clear in my head, although my recent blinding flash of
obviousness that M a is a type, and that of course types can do
interesting things, I think gets me further along.