Here F is the identity functor, and G is the list functor. And yes, C=D=
category of (a subset of) Haskell types.

Are you saying the function that goes from list functor to singleton funtor is a natural transformation? 

But aren't they functors to different subset of Haskell Types?

The Haskell Wikibooks also says the same thing:
Functors in Haskell are from Hask to func, where func is the subcategory of Hask defined on just that functor's types. E.g. the list functor goes from Hask to Lst, where Lst is the category containing only list types, that is, [T] for any type T. The morphisms in Lst are functions defined on list types, that is, functions [T] -> [U] for types T, U.


So in your example there is C that is Hask.  But there are two D's,  D1 that is all List types, and D2 all singleton types.  In this example I guess, the  Singleton types are subset of List types which are subset of Hask.     Is that related to natural transformation or unrelated?

Daryoush


On Wed, Apr 22, 2009 at 12:18 AM, Kim-Ee Yeoh <a.biurvOir4@asuhan.com> wrote:


Daryoush Mehrtash-2 wrote:
>
> I am not sure I follow how the endofunctor gave me the 2nd functor.
>
> As I read the transformation there are two catagories C and D and two
> functors F and G between the same two catagories.  My problem is that I
> only
> have one functor between the Hask and List catagories.  So where does the
> 2nd functor come into picture that also maps between the same C and D
> catagories?
>

Consider
singleton :: a -> [a]
singleton x = [x]

Here F is the identity functor, and G is the list functor. And yes, C=D=
category of (a subset of) Haskell types.

--
View this message in context: http://www.nabble.com/Functor-and-Haskell-tp23166441p23170956.html
Sent from the Haskell - Haskell-Cafe mailing list archive at Nabble.com.

_______________________________________________
Haskell-Cafe mailing list
Haskell-Cafe@haskell.org
http://www.haskell.org/mailman/listinfo/haskell-cafe



--
Daryoush

Weblog:  http://perlustration.blogspot.com/