diff --git a/CHANGELOG.md b/CHANGELOG.md
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,6 +1,10 @@
+# 0.5.0.2 (2021-01-02)
+
+* Compatibility with GHC-9.0 and GHC-9.2.
+
 # 0.5.0.1 (2020-03-29)
 
-* Compatiblity with GHC-8.10 (thanks to Ryan Scott).
+* Compatibility with GHC-8.10 (thanks to Ryan Scott).
 
 # 0.5.0.0 (2019-05-09)
 
diff --git a/sop-core.cabal b/sop-core.cabal
--- a/sop-core.cabal
+++ b/sop-core.cabal
@@ -1,5 +1,5 @@
 name:                sop-core
-version:             0.5.0.1
+version:             0.5.0.2
 synopsis:            True Sums of Products
 description:
   Implementation of n-ary sums and n-ary products.
@@ -25,7 +25,7 @@
 build-type:          Simple
 cabal-version:       >=1.10
 extra-source-files:  CHANGELOG.md doctest.sh
-tested-with:         GHC == 8.0.2, GHC == 8.2.2, GHC == 8.4.4, GHC == 8.6.5, GHC == 8.8.2, GHC == 8.10.1
+tested-with:         GHC == 8.0.2, GHC == 8.2.2, GHC == 8.4.4, GHC == 8.6.5, GHC == 8.8.2, GHC == 8.10.4, GHC == 9.0.1, GHC == 9.2.1
 
 source-repository head
   type:                git
@@ -41,7 +41,7 @@
                        Data.SOP.NP
                        Data.SOP.NS
                        Data.SOP.Sing
-  build-depends:       base                 >= 4.9  && < 4.15,
+  build-depends:       base                 >= 4.9  && < 4.17,
                        deepseq              >= 1.3  && < 1.5
   hs-source-dirs:      src
   default-language:    Haskell2010
diff --git a/src/Data/SOP.hsig b/src/Data/SOP.hsig
deleted file mode 100644
--- a/src/Data/SOP.hsig
+++ /dev/null
@@ -1,7 +0,0 @@
-signature Data.SOP where
-
-data NP :: (k -> Type) -> [k] -> Type where
-  Nil  :: NP f '[]
-  (:*) :: f x -> NP f xs -> NP f (x ': xs)
-
-infixr 5 :*
diff --git a/src/Data/SOP/BasicFunctors.hs b/src/Data/SOP/BasicFunctors.hs
--- a/src/Data/SOP/BasicFunctors.hs
+++ b/src/Data/SOP/BasicFunctors.hs
@@ -56,6 +56,8 @@
 import Control.DeepSeq (NFData1(..), NFData2(..))
 #endif
 
+import Data.Coerce (coerce)
+
 -- * Basic functors
 
 -- | The constant type functor.
@@ -110,7 +112,9 @@
 -- | @since 0.4.0.0
 instance Monoid a => Monoid (K a b) where
   mempty              = K mempty
+#if !MIN_VERSION_base(4,11,0)
   mappend (K x) (K y) = K (mappend x y)
+#endif
 
 instance Monoid a => Applicative (K a) where
   pure _      = K mempty
@@ -134,14 +138,15 @@
 -- | @since 0.4.0.0
 instance Monoid a => Monoid (I a) where
   mempty              = I mempty
+#if !MIN_VERSION_base(4,11,0)
   mappend (I x) (I y) = I (mappend x y)
+#endif
 
 instance Applicative I where
   pure = I
   I f <*> I x = I (f x)
 
 instance Monad I where
-  return = I
   I x >>= f = f x
 
 
@@ -185,7 +190,9 @@
 -- | @since 0.4.0.0
 instance (Monoid (f (g x))) => Monoid ((f :.: g) x) where
   mempty                    = Comp mempty
+#if !MIN_VERSION_base(4,11,0)
   mappend (Comp x) (Comp y) = Comp (mappend x y)
+#endif
 
 instance (Functor f, Functor g) => Functor (f :.: g) where
   fmap f (Comp x) = Comp (fmap (fmap f) x)
@@ -274,19 +281,12 @@
 
 -- * Mapping functions
 
--- Implementation note:
---
--- All of these functions are just type specializations of
--- 'coerce'. However, we currently still support GHC 7.6
--- which does not support 'coerce', so we write them
--- explicitly.
-
 -- | Lift the given function.
 --
 -- @since 0.2.5.0
 --
 mapII :: (a -> b) -> I a -> I b
-mapII = \ f (I a) -> I (f a)
+mapII = coerce
 {-# INLINE mapII #-}
 
 -- | Lift the given function.
@@ -294,7 +294,7 @@
 -- @since 0.2.5.0
 --
 mapIK :: (a -> b) -> I a -> K b c
-mapIK = \ f (I a) -> K (f a)
+mapIK = coerce
 {-# INLINE mapIK #-}
 
 -- | Lift the given function.
@@ -302,7 +302,7 @@
 -- @since 0.2.5.0
 --
 mapKI :: (a -> b) -> K a c -> I b
-mapKI = \ f (K a) -> I (f a)
+mapKI = coerce
 {-# INLINE mapKI #-}
 
 -- | Lift the given function.
@@ -310,7 +310,7 @@
 -- @since 0.2.5.0
 --
 mapKK :: (a -> b) -> K a c -> K b d
-mapKK = \ f (K a) -> K (f a)
+mapKK = coerce
 {-# INLINE mapKK #-}
 
 -- | Lift the given function.
@@ -318,7 +318,7 @@
 -- @since 0.2.5.0
 --
 mapIII :: (a -> b -> c) -> I a -> I b -> I c
-mapIII = \ f (I a) (I b) -> I (f a b)
+mapIII = coerce
 {-# INLINE mapIII #-}
 
 -- | Lift the given function.
@@ -326,7 +326,7 @@
 -- @since 0.2.5.0
 --
 mapIIK :: (a -> b -> c) -> I a -> I b -> K c d
-mapIIK = \ f (I a) (I b) -> K (f a b)
+mapIIK = coerce
 {-# INLINE mapIIK #-}
 
 -- | Lift the given function.
@@ -334,7 +334,7 @@
 -- @since 0.2.5.0
 --
 mapIKI :: (a -> b -> c) -> I a -> K b d -> I c
-mapIKI = \ f (I a) (K b) -> I (f a b)
+mapIKI = coerce
 {-# INLINE mapIKI #-}
 
 -- | Lift the given function.
@@ -342,7 +342,7 @@
 -- @since 0.2.5.0
 --
 mapIKK :: (a -> b -> c) -> I a -> K b d -> K c e
-mapIKK = \ f (I a) (K b) -> K (f a b)
+mapIKK = coerce
 {-# INLINE mapIKK #-}
 
 -- | Lift the given function.
@@ -350,7 +350,7 @@
 -- @since 0.2.5.0
 --
 mapKII :: (a -> b -> c) -> K a d -> I b -> I c
-mapKII = \ f (K a) (I b) -> I (f a b)
+mapKII = coerce
 {-# INLINE mapKII #-}
 
 -- | Lift the given function.
@@ -358,7 +358,7 @@
 -- @since 0.2.5.0
 --
 mapKIK :: (a -> b -> c) -> K a d -> I b -> K c e
-mapKIK = \ f (K a) (I b) -> K (f a b)
+mapKIK = coerce
 {-# INLINE mapKIK #-}
 
 -- | Lift the given function.
@@ -366,7 +366,7 @@
 -- @since 0.2.5.0
 --
 mapKKI :: (a -> b -> c) -> K a d -> K b e -> I c
-mapKKI = \ f (K a) (K b) -> I (f a b)
+mapKKI = coerce
 {-# INLINE mapKKI #-}
 
 -- | Lift the given function.
@@ -374,5 +374,5 @@
 -- @since 0.2.5.0
 --
 mapKKK :: (a -> b -> c) -> K a d -> K b e -> K c f
-mapKKK = \ f (K a) (K b) -> K (f a b)
+mapKKK = coerce
 {-# INLINE mapKKK #-}
diff --git a/src/Data/SOP/Classes.hs b/src/Data/SOP/Classes.hs
--- a/src/Data/SOP/Classes.hs
+++ b/src/Data/SOP/Classes.hs
@@ -294,7 +294,7 @@
 --
 hcliftA  :: (AllN (Prod h) c xs, HAp h)               => proxy c -> (forall a. c a => f a -> f' a)                                                   -> h f   xs -> h f'   xs
 
--- | Variant of 'hcliftA2' that takes a constrained function.
+-- | Variant of 'hliftA2' that takes a constrained function.
 --
 -- /Specification:/
 --
@@ -304,7 +304,7 @@
 --
 hcliftA2 :: (AllN (Prod h) c xs, HAp h, HAp (Prod h)) => proxy c -> (forall a. c a => f a -> f' a -> f'' a)           -> Prod h f xs                 -> h f'  xs -> h f''  xs
 
--- | Variant of 'hcliftA3' that takes a constrained function.
+-- | Variant of 'hliftA3' that takes a constrained function.
 --
 -- /Specification:/
 --
@@ -455,7 +455,7 @@
   --
   hctraverse' :: (AllN h c xs, Applicative g) => proxy c -> (forall a. c a => f a -> g (f' a)) -> h f xs -> g (h f' xs)
 
-  -- | Unconstrained variant of `htraverse'`.
+  -- | Unconstrained variant of `hctraverse'`.
   --
   -- /Instances:/
   --
diff --git a/src/Data/SOP/Constraint.hs b/src/Data/SOP/Constraint.hs
--- a/src/Data/SOP/Constraint.hs
+++ b/src/Data/SOP/Constraint.hs
@@ -154,7 +154,7 @@
 --
 -- /Example:/ The constraint
 --
--- > All (~) '[ Int, Bool, Char ] '[ a, b, c ]
+-- > AllZip (~) '[ Int, Bool, Char ] '[ a, b, c ]
 --
 -- is equivalent to the constraint
 --
diff --git a/src/Data/SOP/NP.hs b/src/Data/SOP/NP.hs
--- a/src/Data/SOP/NP.hs
+++ b/src/Data/SOP/NP.hs
@@ -159,7 +159,9 @@
 #endif
   ) => Monoid (NP f xs) where
   mempty  = cpure_NP (Proxy :: Proxy (Monoid `Compose` f)) mempty
+#if !MIN_VERSION_base(4,11,0)
   mappend = czipWith_NP (Proxy :: Proxy (Monoid `Compose` f)) mappend
+#endif
 
 -- | @since 0.2.5.0
 instance All (NFData `Compose` f) xs => NFData (NP f xs) where
@@ -193,7 +195,9 @@
 -- | @since 0.4.0.0
 instance (Monoid (NP (NP f) xss)) => Monoid (POP f xss) where
   mempty                      = POP mempty
+#if !MIN_VERSION_base(4,11,0)
   mappend (POP xss) (POP yss) = POP (mappend xss yss)
+#endif
 
 -- | @since 0.2.5.0
 instance (NFData (NP (NP f) xss)) => NFData (POP f xss) where