diff --git a/CHANGELOG b/CHANGELOG
--- a/CHANGELOG
+++ b/CHANGELOG
@@ -1,5 +1,9 @@
 CHANGELOG
 
+1.1.2 -> 1.2
+  - Add support for GHC 9.0, drop GHC 8.8
+  - Update to derive-lifted-instances v0.2.2
+
 1.1.1 -> 1.1.2
   - Update to derive-lifted-instances v0.2
   - Add deriving instances for `Cofree`, `HCofree` and `HHCofree`
diff --git a/examples/Sem.hs b/examples/Sem.hs
--- a/examples/Sem.hs
+++ b/examples/Sem.hs
@@ -1,6 +1,6 @@
-{-# LANGUAGE TemplateHaskell, UndecidableInstances, QuantifiedConstraints, FlexibleInstances #-}
+{-# LANGUAGE TemplateHaskell, UndecidableInstances, QuantifiedConstraints, ConstraintKinds, FlexibleInstances #-}
 module Sem where
-  
+
 import Data.Functor.Free
 
 class BaseSem a where
diff --git a/free-functors.cabal b/free-functors.cabal
--- a/free-functors.cabal
+++ b/free-functors.cabal
@@ -1,5 +1,5 @@
 name:                free-functors
-version:             1.1.2
+version:             1.2
 synopsis:            Free functors, adjoint to functors that forget class constraints.
 description:         A free functor is a left adjoint to a forgetful functor. It used to be the case
                      that the only category that was easy to work with in Haskell was Hask itself, so
@@ -22,6 +22,7 @@
 
 build-type:          Simple
 cabal-version:       >= 1.10
+tested-with:         GHC==9.0.0.20200925, GHC==8.10.2
 
 extra-source-files:
   examples/*.hs
@@ -45,11 +46,11 @@
     Haskell2010
 
   build-depends:
-    base >= 4.13 && < 4.15,
-    template-haskell >= 2.15 && < 2.17,
+    base >= 4.14 && < 4.16,
+    template-haskell >= 2.16 && < 2.18,
     transformers == 0.5.*,
     comonad == 5.*,
-    derive-lifted-instances >= 0.2 && < 0.3,
+    derive-lifted-instances >= 0.2.2 && < 0.3,
     contravariant == 1.5.*,
     bifunctors == 5.*,
     profunctors == 5.*
diff --git a/src/Data/Functor/Cofree/Internal.hs b/src/Data/Functor/Cofree/Internal.hs
--- a/src/Data/Functor/Cofree/Internal.hs
+++ b/src/Data/Functor/Cofree/Internal.hs
@@ -15,6 +15,7 @@
   , QuantifiedConstraints
   , MultiParamTypeClasses
   , UndecidableSuperClasses
+  , StandaloneKindSignatures
   #-}
 module Data.Functor.Cofree.Internal where
 
@@ -22,6 +23,7 @@
 
 import Language.Haskell.TH.Syntax
 import Data.DeriveLiftedInstances
+import Data.Kind (Constraint)
 
 
 kExp :: Q Exp
@@ -41,9 +43,7 @@
 deriveCofreeInstance' :: Name -> Name -> Name -> Q [Dec]
 deriveCofreeInstance' (pure . ConT -> cofree) ccofree (pure . ConT -> clss)
   = deriveInstance (cofreeDeriv ccofree)
-      [t| forall a c. (c ~=> $clss) => $clss ($cofree c a) |]
-
-class (a => b) => a :=> b
-instance (a => b) => a :=> b
+      [t| forall a c. (c ~=> $clss, c ($cofree c a)) => $clss ($cofree c a) |]
 
-type a ~=> b = forall x. a x :=> b x
+type (~=>) :: (k -> Constraint) -> (k -> Constraint) -> Constraint
+type a ~=> b = forall x. a x => b x
diff --git a/src/Data/Functor/Free/Internal.hs b/src/Data/Functor/Free/Internal.hs
--- a/src/Data/Functor/Free/Internal.hs
+++ b/src/Data/Functor/Free/Internal.hs
@@ -15,6 +15,7 @@
   , QuantifiedConstraints
   , MultiParamTypeClasses
   , UndecidableSuperClasses
+  , StandaloneKindSignatures
   #-}
 module Data.Functor.Free.Internal where
 
@@ -22,6 +23,7 @@
 
 import Language.Haskell.TH.Syntax
 import Data.DeriveLiftedInstances
+import Data.Kind (Constraint)
 
 
 kExp :: Q Exp
@@ -40,7 +42,7 @@
 deriveFreeInstance' (pure . ConT -> free) cfree runFree (pure . ConT -> clss)
   = deriveInstance
       (freeDeriv cfree runFree)
-      [t| forall a c. (c ~=> $clss) => $clss ($free c a) |]
+      [t| forall a c. (c ~=> $clss, c ($free c a)) => $clss ($free c a) |]
 
 deriveInstances' :: Name -> Name -> Name -> Name -> Q [Dec]
 deriveInstances' tfree cfree runFree nm@(pure . ConT -> clss) =
@@ -50,7 +52,5 @@
     , deriveInstance (apDeriv idDeriv) [t| forall f a c. (Applicative f, $clss a) => $clss (Ap f a) |]
     ]
 
-class (a => b) => a :=> b
-instance (a => b) => a :=> b
-
-type a ~=> b = forall x. a x :=> b x
+type (~=>) :: (k -> Constraint) -> (k -> Constraint) -> Constraint
+type a ~=> b = forall x. a x => b x
diff --git a/src/Data/Functor/HCofree.hs b/src/Data/Functor/HCofree.hs
--- a/src/Data/Functor/HCofree.hs
+++ b/src/Data/Functor/HCofree.hs
@@ -40,7 +40,13 @@
 data HCofree c g a where
   HCofree :: c f => (f :~> g) -> f a -> HCofree c g a
 
+-- | The cofree comonad of a functor.
+instance (c ~=> Comonad, c (HCofree c g)) => Comonad (HCofree c g) where
+  extract (HCofree _ a) = extract a
+  extend f (HCofree k a) = HCofree k $ extend (f . HCofree k) a
+  duplicate (HCofree k a) = HCofree k $ extend (HCofree k) a
 
+
 -- | Derive the instance of @`HCofree` c a@ for the class @c@.
 --
 -- For example:
@@ -54,7 +60,7 @@
 counit (HCofree k fa) = k fa
 
 leftAdjunct :: c f => (f :~> g) -> f :~> HCofree c g
-leftAdjunct = HCofree
+leftAdjunct f = HCofree f
 
 -- | @unit = leftAdjunct id@
 unit :: c g => g :~> HCofree c g
@@ -68,7 +74,7 @@
 transform t (HCofree k a) = HCofree (t k) a
 
 hfmap :: (f :~> g) -> HCofree c f :~> HCofree c g
-hfmap f = transform (f .)
+hfmap f = transform (\g -> f . g)
 
 hextend :: (HCofree c f :~> g) -> HCofree c f :~> HCofree c g
 hextend f = transform (\k -> f . leftAdjunct k)
@@ -91,9 +97,3 @@
 deriveCofreeInstance' ''HCofree 'HCofree ''Functor
 deriveCofreeInstance' ''HCofree 'HCofree ''Foldable
 deriveCofreeInstance' ''HCofree 'HCofree ''Traversable
-
--- | The cofree comonad of a functor.
-instance (c ~=> Comonad) => Comonad (HCofree c g) where
-  extract (HCofree _ a) = extract a
-  extend f (HCofree k a) = HCofree k $ extend (f . HCofree k) a
-  duplicate (HCofree k a) = HCofree k $ extend (HCofree k) a
diff --git a/src/Data/Functor/HFree.hs b/src/Data/Functor/HFree.hs
--- a/src/Data/Functor/HFree.hs
+++ b/src/Data/Functor/HFree.hs
@@ -41,7 +41,13 @@
 -- | The higher order free functor for constraint @c@.
 newtype HFree c f a = HFree { runHFree :: forall g. c g => (f :~> g) -> g a }
 
+-- | The free monad of a functor.
+instance (c ~=> Monad, c (HFree c f)) => Monad (HFree c f) where
+  return = pure
+  HFree f >>= g = HFree $ \k -> f k >>= rightAdjunct k . g
+  HFree f >> HFree g = HFree $ \k -> f k >> g k
 
+
 -- | Derive the instance of @`HFree` c f a@ for the class @c@,.
 --
 -- For example:
@@ -50,7 +56,6 @@
 deriveHFreeInstance :: Name -> Q [Dec]
 deriveHFreeInstance = deriveFreeInstance' ''HFree 'HFree 'runHFree
 
-
 unit :: f :~> HFree c f
 unit fa = HFree $ \k -> k fa
 
@@ -70,7 +75,7 @@
 -- transform t = HFree . (. t) . runHFree
 
 hfmap :: (f :~> g) -> HFree c f :~> HFree c g
-hfmap f = transform (. f)
+hfmap f = transform (\g -> g . f)
 
 bind :: (f :~> HFree c g) -> HFree c f :~> HFree c g
 bind f = transform (\k -> rightAdjunct k . f)
@@ -94,9 +99,6 @@
 deriveFreeInstance' ''HFree 'HFree 'runHFree ''Functor
 deriveFreeInstance' ''HFree 'HFree 'runHFree ''Applicative
 deriveFreeInstance' ''HFree 'HFree 'runHFree ''Alternative
-
--- | The free monad of a functor.
-deriveFreeInstance' ''HFree 'HFree 'runHFree ''Monad
 
 -- HFree Monad is only a monad transformer if rightAdjunct is called with monad morphisms.
 -- F.e. lift . return == return fails if the results are inspected with rightAdjunct (const Nothing).
diff --git a/src/Data/Functor/HHCofree.hs b/src/Data/Functor/HHCofree.hs
--- a/src/Data/Functor/HHCofree.hs
+++ b/src/Data/Functor/HHCofree.hs
@@ -60,7 +60,7 @@
 counit (HHCofree k fa) = k fa
 
 leftAdjunct :: c f => (f :~~> g) -> f :~~> HHCofree c g
-leftAdjunct = HHCofree
+leftAdjunct f = HHCofree f
 
 -- | @unit = leftAdjunct id@
 unit :: c g => g :~~> HHCofree c g
@@ -74,7 +74,7 @@
 transform t (HHCofree k a) = HHCofree (t k) a
 
 hfmap :: (f :~~> g) -> HHCofree c f :~~> HHCofree c g
-hfmap f = transform (f .)
+hfmap f = transform (\g -> f . g)
 
 hextend :: (HHCofree c f :~~> g) -> HHCofree c f :~~> HHCofree c g
 hextend f = transform (\k -> f . leftAdjunct k)
diff --git a/src/Data/Functor/HHFree.hs b/src/Data/Functor/HHFree.hs
--- a/src/Data/Functor/HHFree.hs
+++ b/src/Data/Functor/HHFree.hs
@@ -72,7 +72,7 @@
 -- transform t = HHFree . (. t) . runHHFree
 
 hfmap :: (f :~~> g) -> HHFree c f :~~> HHFree c g
-hfmap f = transform (. f)
+hfmap f = transform (\g -> g . f)
 
 bind :: (f :~~> HHFree c g) -> HHFree c f :~~> HHFree c g
 bind f = transform (\k -> rightAdjunct k . f)
@@ -99,8 +99,8 @@
 deriveFreeInstance' ''HHFree 'HHFree 'runHHFree ''ArrowChoice
 deriveFreeInstance' ''HHFree 'HHFree 'runHHFree ''ArrowLoop
 
-instance (forall x. c x => ArrowApply x) => ArrowApply (HHFree c f) where
-  app = HHFree $ \k -> app . arr (first (rightAdjunct k))
+instance (c ~=> ArrowApply, c (HHFree c f)) => ArrowApply (HHFree c f) where
+  app = HHFree $ \k -> app . arr (\(a, b) -> (rightAdjunct k a, b))
 
 deriveFreeInstance' ''HHFree 'HHFree 'runHHFree ''Bifunctor
 deriveFreeInstance' ''HHFree 'HHFree 'runHHFree ''Biapplicative