diff --git a/pointed.cabal b/pointed.cabal
--- a/pointed.cabal
+++ b/pointed.cabal
@@ -1,6 +1,6 @@
 name:          pointed
 category:      Data
-version:       4.1.1
+version:       4.2
 license:       BSD3
 cabal-version: >= 1.6
 license-file:  LICENSE
@@ -27,6 +27,7 @@
     containers           >= 0.4     && < 0.6,
     comonad              >= 4       && < 5,
     data-default-class   >= 0.0.1   && < 0.1,
+    kan-extensions       >= 4.2     && < 5,
     semigroups           >= 0.8.3.1 && < 1,
     semigroupoids        >= 4       && < 5,
     stm                  >= 2.1.2.1 && < 2.5,
diff --git a/src/Data/Copointed.hs b/src/Data/Copointed.hs
--- a/src/Data/Copointed.hs
+++ b/src/Data/Copointed.hs
@@ -1,6 +1,7 @@
 {-# LANGUAGE CPP #-}
+{-# LANGUAGE TypeFamilies #-}
 #if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 702
-{-# LANGUAGE Trustworthy #-}
+{-# LANGUAGE Safe #-}
 #endif
 module Data.Copointed where
 
@@ -8,6 +9,7 @@
 import Data.Functor.Identity
 import Data.Functor.Compose
 import Data.Functor.Coproduct
+import Data.Functor.Kan.Lift
 import qualified Data.Functor.Sum as F
 import Data.Tree
 import Data.Semigroup as Semigroup
@@ -59,6 +61,10 @@
 
 instance (Copointed p, Copointed q) => Copointed (Coproduct p q) where
   copoint = coproduct copoint copoint
+
+instance (Functor g, g ~ h) => Copointed (Lift g h) where
+  copoint x = runIdentity (runLift x (fmap Identity))
+  {-# INLINE copoint #-}
 
 instance Copointed m => Copointed (IdentityT m) where
   copoint = copoint . runIdentityT
diff --git a/src/Data/Pointed.hs b/src/Data/Pointed.hs
--- a/src/Data/Pointed.hs
+++ b/src/Data/Pointed.hs
@@ -1,6 +1,7 @@
 {-# LANGUAGE CPP #-}
+{-# LANGUAGE TypeFamilies #-}
 #if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 702
-{-# LANGUAGE Trustworthy #-}
+{-# LANGUAGE Safe #-}
 #endif
 module Data.Pointed where
 
@@ -17,6 +18,7 @@
 import Data.Set (Set)
 import qualified Data.Set as Set
 import Data.Functor.Constant
+import Data.Functor.Kan.Rift
 import qualified Data.Functor.Product as Functor
 import Data.Functor.Compose
 import Data.Functor.Reverse
@@ -138,6 +140,10 @@
 
 instance Pointed (Lift f) where
   point = Pure
+
+instance (Functor g, g ~ h) => Pointed (Rift g h) where
+  point a = Rift (fmap ($a))
+  {-# INLINE point #-}
 
 instance (Pointed p, Pointed q) => Pointed (Functor.Product p q) where
   point a = Functor.Pair (point a) (point a)