[Haskell-beginners] Functors in Haskell

[Dimitri DeFigueiredo]

Hi All,

I'm trying to merge in my head the concepts of:

- functors from category theory; with,
- the Functor typeclass in haskell.

Here's what I have come up with:

A Functor F in haskell is a type constructor that provides a functor map 
(fmap) and that maps Hask (the category of haskell types) into a 
category generated by the Functor. For example, Maybe maps the category 
of all haskell types "a" (i.e. Hask) into the category of all types of 
the form "Maybe a" by providing an implementation of fmap.

Neglecting the fact that apparently Hask isn't a category, does this 
sound reasonable? I think the insight for me here is that functors in 
haskell are type constructors mapping Hask into another category. Is 
that a good way to think about it?

Thanks!

Dimitri