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?