Semigroup/Monoid/Semigroupoid/Category/Endo

gistfile1.hs

class Semigroupoid cat where
  (<.>) ::
    cat a b
    -> cat b c
    -> cat a c

class Semigroupoid cat => Category cat where
  identity ::
    cat a a

class Semigroup s where
  (<>) ::
    s
    -> s
    -> s

class Semigroup s => Monoid s where
  zero :: 
    s

newtype Endo hom a = Endo (hom a a)

instance Semigroupoid hom => Semigroup (Endo hom a) where
  Endo x <> Endo y =
    Endo (x <.> y)

instance Category hom => Monoid (Endo hom a) where
  zero =
    Endo identity