On Wed, Jul 8, 2009 at 4:02 AM, Ross Paterson <ross@soi.city.ac.uk> wrote:

On Tue, Jul 07, 2009 at 11:33:25PM -0400, roconnor@theorem.ca wrote:
> I suggest adding a wrapper to make (a x x) a Monoid for any Category a
> and type x. This would be added to Control.Category.
>
> newtype EndoCategory a x = EndoCategory { runEndoCategory :: a x x }
>
> instance (Category a) => Monoid (EndoCategory a x) where
> mempty = EndoCategory id
> mappend (EndoCategory f) (EndoCategory g) = EndoCategory (f . g)

In Data.Monoid there is

newtype Endo a = Endo { appEndo :: a -> a }

instance Monoid (Endo a) where
mempty = Endo id
Endo f `mappend` Endo g = Endo (f . g)

and (->) is an instance of Category, so perhaps we should generalize Endo.

The name EndoCategory seems wrong, as this won't be an instance of Category.
Endomorphism?

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