On Mon, Jan 17, 2011 at 9:46 PM, C K Kashyap <ckkash...@gmail.com> wrote:
> > I am not able to fully understand how those diagrams translate to haskell - > I can guess that T^2 -> T referes to things like concat operation but not > able to relate it to bind. > > I found it useful to work out the correspondence between monoids and monads; lots of introductory texts on CT give the example of the category Mon so I won't bore you with an account here. Thinking about monoids and monads helped me move past element-centric thinking toward the arrow-centric way of thinking in CT. In particular it's helpful to work out how the mu operator of a monad (which composes arrows) is a kind of abstraction of monoid operators (which combine elements). What you end up with is the monad as a device you can use to make non-monoidal things behave like monoids - closure, associativity, identity. For bind, google around for Kleisli Category and Kleisli star. I think of the latter as a kind of hybrid of a function and a functor, although I'm not entirely sure that's correct. -Gregg
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