diff --git a/Data/Universe.hs b/Data/Universe.hs
--- a/Data/Universe.hs
+++ b/Data/Universe.hs
@@ -23,8 +23,7 @@
 import Control.Monad.Reader
 import Control.Monad.Trans.Identity
 import Data.Functor.Compose
-import Data.Functor.Representable
-import Data.Key (Key)
+import Data.Functor.Rep
 import qualified Data.Functor.Product as Functor
 
 -- | Creating an instance of this class is a declaration that your type is
@@ -127,7 +126,7 @@
 
 -- We could do this:
 --
--- instance Universe (f a) => Universe (Rep f a) where universe = map Rep universe
+-- instance Universe (f a) => Universe (Co f a) where universe = map Rep universe
 --
 -- However, since you probably only apply Rep to functors when you want to
 -- think of them as being representable, I think it makes sense to use an
@@ -135,10 +134,10 @@
 -- universe-ness.
 --
 -- Please complain if you disagree!
-instance (Representable f, Finite (Key f), Ord (Key f), Universe a)
-	=> Universe (Rep f a)
+instance (Representable f, Finite (Rep f), Ord (Rep f), Universe a)
+	=> Universe (Co f a)
 	where universe = map tabulate universe
-instance (Representable f, Finite s, Ord s, Finite (Key f), Ord (Key f), Universe a)
+instance (Representable f, Finite s, Ord s, Finite (Rep f), Ord (Rep f), Universe a)
 	=> Universe (TracedT s f a)
 	where universe = map tabulate universe
 
@@ -185,10 +184,10 @@
 instance  Finite (f (g a))               => Finite (Compose f g a) where universeF = map Compose   universeF
 instance (Finite (f a), Finite (g a))    => Finite (Functor.Product f g a) where universeF = liftM2 Functor.Pair universeF universeF
 
-instance (Representable f, Finite (Key f), Ord (Key f), Finite a)
-	=> Finite (Rep f a)
+instance (Representable f, Finite (Rep f), Ord (Rep f), Finite a)
+	=> Finite (Co f a)
 	where universeF = map tabulate universeF
-instance (Representable f, Finite s, Ord s, Finite (Key f), Ord (Key f), Finite a)
+instance (Representable f, Finite s, Ord s, Finite (Rep f), Ord (Rep f), Finite a)
 	=> Finite (TracedT s f a)
 	where universeF = map tabulate universeF
 
diff --git a/universe.cabal b/universe.cabal
--- a/universe.cabal
+++ b/universe.cabal
@@ -1,5 +1,5 @@
 name:                universe
-version:             0.4.0.5
+version:             0.5
 synopsis:            Classes for types where we know all the values
 description:         Munge finite and recursively enumerable types
 license:             BSD3
@@ -16,7 +16,7 @@
 source-repository this
     type:            git
     location:        https://github.com/dmwit/universe
-    tag:             0.4.0.5
+    tag:             0.5
 
 library
   exposed-modules:     Data.Universe,
@@ -30,10 +30,10 @@
   if impl(ghc >= 7.4)
     cpp-options:       -DDEFAULT_SIGNATURES
   build-depends:       base                   >=4   && <5  ,
-                       comonad-transformers   >=0.1 && <4.0,
+                       comonad                >=4   && <4.1,
                        containers             >=0.1 && <1  ,
                        keys                   >=0.1 && <4  ,
                        mtl                    >=1.0 && <2.2,
-                       representable-functors >=2.4 && <3.3,
+                       adjunctions            >=4   && <4.1,
                        transformers           >=0.2 && <0.4,
                        void                   >=0.1 && <0.7