https://fumieval.github.io/papers/en/2015-Haskell-objects.pdf

Object.hs

{-# LANGUAGE RankNTypes #-}
import Prelude hiding (id, (.))
import Control.Category
import Data.Functor.Coyoneda
import Data.Bifunctor (first)

newtype Object f g = Object { runObject :: forall a. f a -> g (Object f g, a) }
newtype Obj f g = Obj { runObj :: forall a. f a -> Coyoneda g (Obj f g, a) }

to :: Object f g -> Obj f g
to (Object n) = Obj $ fmap (first to) . liftCoyoneda . n

from :: Functor g => Obj f g -> Object f g
from (Obj n) = Object $ lowerCoyoneda . fmap (first from) . n

instance Category Obj where
  id = Obj $ fmap ((,) id) . liftCoyoneda
  Obj l . Obj r = Obj $ \fa -> case r fa of
      Coyoneda f ga -> case l ga of
        Coyoneda g ha -> Coyoneda (comp g f) ha
    where
      comp :: (s0 -> (Obj g h, s1)) -> (s1 -> (Obj f g, s2)) -> s0 -> (Obj f h, s2)
      comp sgh sfg s0 =
        let (gh, s1) = sgh s0 in
        let (fg, s2) = sfg s1 in
            (gh . fg, s2)