<div class="gmail_quote">On Mon, Jan 17, 2011 at 9:46 PM, C K Kashyap <span dir="ltr"><<a href="mailto:ckkashyap@gmail.com" target="_blank">ckkashyap@gmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div><br></div><div>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.</div>
<div><br></div></blockquote><div>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.</div>
<div><br></div><div>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.</div><div><br>
</div><div>-Gregg</div></div>