[Haskell-cafe] Functor and Haskell
wren ng thornton
wren at freegeek.org
Tue Apr 21 23:03:12 EDT 2009
Daryoush Mehrtash 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
You don't have a category List, you have the image of the List functor
(in Hask). With the definition:
data List a =...
instance Functor List where fmap =...
The type constructor "List" provides the object half of an endofunctor
on Hask, and the function "fmap @List" provides the morphism half of the
Now, if you declare another endofunctor, G:
data G a =...
instance Functor G where fmap =...
then a natural transformation from List to G must provide a mapping
(forall a. List a -> G a) for objects and a mapping (forall a b. (List a
-> List b) -> (G a -> G b)) for morphisms, satisfying all the necessary
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