Re: [Haskell-cafe] Re: Monads that are Comonads and the role of Adjunction

2007-12-17 Thread Yitzchak Gale
Derek Elkins wrote: There is another very closely related adjunction that is less often mentioned. ((-)-C)^op -| (-)-C or a - b - C ~ b - a - C This gives rise to the monad, M a = (a - C) - C this is also exactly the comonad it gives rise to (in the op category which ends up being the

Re: [Haskell-cafe] Re: Monads that are Comonads and the role of Adjunction

2007-12-17 Thread David Menendez
On Dec 17, 2007 4:34 AM, Yitzchak Gale [EMAIL PROTECTED] wrote: Derek Elkins wrote: There is another very closely related adjunction that is less often mentioned. ((-)-C)^op -| (-)-C or a - b - C ~ b - a - C This gives rise to the monad, M a = (a - C) - C this is also exactly

Re: [Haskell-cafe] Re: Monads that are Comonads and the role of Adjunction

2007-12-17 Thread Derek Elkins
On Mon, 2007-12-17 at 09:58 -0500, David Menendez wrote: On Dec 17, 2007 4:34 AM, Yitzchak Gale [EMAIL PROTECTED] wrote: Derek Elkins wrote: There is another very closely related adjunction that is less often mentioned. ((-)-C)^op -|

[Haskell-cafe] Re: Monads that are Comonads and the role of Adjunction

2007-12-16 Thread apfelmus
Dan Weston wrote: newtype O f g a = O (f (g a)) -- Functor composition: f `O` g instance (Functor f, Functor g) = Functor (O f g) where ... instance Adjunction f g = Monad (O g f) where ... instance Adjunction f g = Comonad (O f g) where ... class (Functor f, Functor g)

Re: [Haskell-cafe] Re: Monads that are Comonads and the role of Adjunction

2007-12-16 Thread Derek Elkins
On Sun, 2007-12-16 at 13:49 +0100, apfelmus wrote: Dan Weston wrote: newtype O f g a = O (f (g a)) -- Functor composition: f `O` g instance (Functor f, Functor g) = Functor (O f g) where ... instance Adjunction f g = Monad (O g f) where ... instance Adjunction f g =