diff --git a/CHANGELOG.markdown b/CHANGELOG.markdown
--- a/CHANGELOG.markdown
+++ b/CHANGELOG.markdown
@@ -1,3 +1,11 @@
+4.2.1
+---
+* Add `liftRift` and `lowerRift`
+
+4.2
+---
+* Remove pointed dependency
+
 4.1.1
 ---
 * Added `Applicative` instance for `Day`
diff --git a/kan-extensions.cabal b/kan-extensions.cabal
--- a/kan-extensions.cabal
+++ b/kan-extensions.cabal
@@ -1,6 +1,6 @@
 name:          kan-extensions
 category:      Data Structures, Monads, Comonads, Functors
-version:       4.2
+version:       4.2.1
 license:       BSD3
 cabal-version: >= 1.6
 license-file:  LICENSE
diff --git a/src/Data/Functor/Kan/Rift.hs b/src/Data/Functor/Kan/Rift.hs
--- a/src/Data/Functor/Kan/Rift.hs
+++ b/src/Data/Functor/Kan/Rift.hs
@@ -26,7 +26,7 @@
   , composeRift, decomposeRift
   , adjointToRift, riftToAdjoint
   , composedAdjointToRift, riftToComposedAdjoint
-  , rap
+  , liftRift, lowerRift, rap
   ) where
 
 import Control.Applicative
@@ -110,6 +110,30 @@
   {-# INLINE pure #-}
   Rift mf <*> Rift ma = Rift (ma . mf . fmap (.))
   {-# INLINE (<*>) #-}
+
+-- | The natural isomorphism between @f@ and @Rift f f@.
+-- @
+-- 'lowerRift' '.' 'liftRift' ≡ 'id'
+-- 'liftRift' '.' 'lowerRift' ≡ 'id'
+-- @
+--
+-- @
+-- 'lowerRift' ('liftRift' x)     -- definition
+-- 'lowerRift' ('Rift' ('<*>' x))   -- definition
+-- ('<*>' x) ('pure' 'id')          -- beta reduction
+-- 'pure' 'id' '<*>' x              -- Applicative identity law
+-- x
+-- @
+liftRift :: Applicative f => f a -> Rift f f a
+liftRift fa = Rift (<*> fa)
+{-# INLINE liftRift #-}
+
+-- | Lower 'Rift' by applying 'pure' 'id' to the continuation.
+--
+-- See 'liftRift'.
+lowerRift :: Applicative f => Rift f g a -> g a
+lowerRift (Rift f) = f (pure id)
+{-# INLINE lowerRift #-}
 
 -- | Indexed applicative composition of right Kan lifts.
 rap :: Functor f => Rift f g (a -> b) -> Rift g h a -> Rift f h b