[Haskell-cafe] morphisms in IO

Gregg Reynolds dev at mobileink.com
Fri Feb 6 01:13:32 EST 2009

On Thu, Feb 5, 2009 at 10:32 PM, Dan Weston <westondan at imageworks.com> wrote:
> I truly have no idea what you are saying (and probably not even what I am
> saying), but I suspect:
> a) You are calling IO the target category of applying the functor IO [taking
> a to IO a and (a->b) to (IO a -> IO b)] to Hask.
> b) This category is hardly bereft, nor discrete. Its morphisms are IO a ->
> IO b.

Well, that's a function in Haskell, yes; but does it represent a
morphism /in/ the category?  It looks more like a Functor morphism to
> c) What you are calling a "bereft" category is an empty category. Without
> (identity) morphisms, there can be no objects. There is only one such

Right, I meant other than Id morphisms.  I guess "discrete" is the correct term.

> category (the empty category), so naturally any two such are isomorphic (for
> what it's worth, which I suspect is not much).



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