module Data.Morphism.Iso where

import Control.Category.Groupoid

data Iso s a b = Iso (s a b) (s b a)
  deriving (Typeable)

instance Category s => Category (Iso s) where
    id = Iso id id
    Iso f f' . Iso g g' = Iso (f . g) (g' . f')

instance Category s => Groupoid (Iso s) where
    invert (Iso f f') = Iso f' f