diff --git a/CHANGELOG.md b/CHANGELOG.md
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,5 +1,9 @@
 # Revision history for squares
 
+## 0.2 -- 2020-07-08
+
+* Added `Data.Functor.Kan.Square`.
+
 ## 0.1.1 -- 2020-05-27
 
 * Added `fromRight2`, `fromLeft2`, `toRight2` and `toLeft2` to `Data.Square`.
diff --git a/squares.cabal b/squares.cabal
--- a/squares.cabal
+++ b/squares.cabal
@@ -1,7 +1,7 @@
 cabal-version:       >=1.10
 
 name:                squares
-version:             0.1.1
+version:             0.2
 synopsis:            The double category of Hask functors and profunctors
 description:         A library for working with natural transformations of type
                      .
@@ -34,6 +34,7 @@
                        Data.Profunctor.Square
                        Data.Traversable.Square
                        Data.Functor.Adjunction.Square
+                       Data.Functor.Kan.Square
                        Data.Functor.Rep.Square
   build-depends:       base >= 4.9 && < 5
                      , profunctors == 5.*
diff --git a/src/Data/Functor/Kan/Square.hs b/src/Data/Functor/Kan/Square.hs
new file mode 100644
--- /dev/null
+++ b/src/Data/Functor/Kan/Square.hs
@@ -0,0 +1,70 @@
+{-# LANGUAGE DataKinds, RankNTypes, GADTs #-}
+-----------------------------------------------------------------------------
+-- |
+-- Module      :  Data.Functor.Kan.Square
+-- License     :  BSD-style (see the file LICENSE)
+-- Maintainer  :  sjoerd@w3future.com
+--
+-----------------------------------------------------------------------------
+module Data.Functor.Kan.Square where
+
+import Data.Square
+import Data.Profunctor
+import Data.Profunctor.Composition
+import Data.Functor.Compose.List
+
+-- | The left Kan extension of a functor @f@ along a profunctor @j@.
+--
+-- The left Kan extension of a functor @f@ along a functor @g@ is @'Lan' ('Data.Profunctor.Costar' g) f@.
+data Lan j f b = forall a. Lan (j a b) (f a)
+
+-- |
+-- > +--f--+
+-- > |  v  |
+-- > j--@  |
+-- > |  v  |
+-- > +--L--+
+lanSquare :: Square '[j] '[] '[f] '[Lan j f]
+lanSquare = mkSquare Lan
+
+-- |
+-- > +--f--+
+-- > |  v  |     +--L--+
+-- > j-\|  |     |  v  |
+-- > |  @  | ==> h--@  |
+-- > h-/|  |     |  v  |
+-- > |  v  |     +--g--+
+-- > +--g--+
+--
+-- Any square like the one on the left factors through 'lanSquare'.
+-- 'lanFactor' gives the remaining square.
+lanFactor :: (Profunctor h, IsFList gs) => Square '[j, h] '[] '[f] gs -> Square '[h] '[] '[Lan j f] gs
+lanFactor sq = mkSquare $ \h (Lan j f) -> runSquare sq (Procompose h j) f
+
+-- | The right Kan extension of a functor @f@ along a profunctor @j@.
+--
+-- The right Kan extension of a functor @f@ along a functor @g@ is @'Ran' ('Data.Profunctor.Star' g) f@.
+newtype Ran j f a = Ran { runRan :: forall b. j a b -> f b }
+
+-- |
+-- > +--R--+
+-- > |  v  |
+-- > j--@  |
+-- > |  v  |
+-- > +--g--+
+ranSquare :: Square '[j] '[] '[Ran j g] '[g]
+ranSquare = mkSquare $ flip runRan
+
+-- |
+-- > +--f--+
+-- > |  v  |     +--f--+
+-- > h-\|  |     |  v  |
+-- > |  @  | ==> h--@  |
+-- > j-/|  |     |  v  |
+-- > |  v  |     +--R--+
+-- > +--g--+
+--
+-- Any square like the one on the left factors through 'ranSquare'.
+-- 'ranFactor' gives the remaining square.
+ranFactor :: (Profunctor j, IsFList fs) => Square '[h, j] '[] fs '[g] -> Square '[h] '[] fs '[Ran j g]
+ranFactor sq = mkSquare $ \h f -> Ran $ \j -> runSquare sq (Procompose j h) f