diff --git a/CHANGELOG.md b/CHANGELOG.md
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,5 +1,10 @@
 # recursion
 
+## 2.2.4.2
+
+* Drop support for Eta
+* Works with GHC 9.0
+
 ## 2.2.4.1
 
 * Add more doctests
diff --git a/recursion.cabal b/recursion.cabal
--- a/recursion.cabal
+++ b/recursion.cabal
@@ -1,6 +1,6 @@
 cabal-version:      1.18
 name:               recursion
-version:            2.2.4.1
+version:            2.2.4.2
 license:            BSD3
 license-file:       LICENSE
 copyright:          Copyright: (c) 2018-2019 Vanessa McHale
@@ -28,7 +28,10 @@
     manual:      True
 
 library
-    exposed-modules:  Control.Recursion
+    exposed-modules:
+        Control.Recursion
+        Control.Recursion.GHC
+
     hs-source-dirs:   src
     default-language: Haskell2010
     other-extensions:
@@ -41,8 +44,8 @@
         base >=4.9 && <5,
         composition-prelude -any
 
-    if !impl(eta -any)
-        exposed-modules: Control.Recursion.GHC
+    if impl(eta -any)
+        buildable: False
 
     if (flag(development) && !impl(ghc >=8.8))
         ghc-options: -Werror
diff --git a/src/Control/Recursion.hs b/src/Control/Recursion.hs
--- a/src/Control/Recursion.hs
+++ b/src/Control/Recursion.hs
@@ -64,12 +64,13 @@
 import           Control.Composition ((.*), (.**))
 import           Control.Monad       ((<=<))
 import           Data.Foldable       (toList)
+import           Data.Kind           (Type)
 import           Data.List.NonEmpty  (NonEmpty (..))
 import qualified Data.List.NonEmpty  as NE
 import           GHC.Generics
 import           Numeric.Natural     (Natural)
 
-type family Base t :: * -> *
+type family Base t :: Type -> Type
 
 class (Functor (Base t)) => Recursive t where
 
@@ -364,6 +365,8 @@
 mcata ψ = mc where mc = ψ mc . unFix
 
 -- | Mendler's histomorphism
+--
+-- See [here](https://dl.acm.org/doi/pdf/10.1145/3409004) for an example
 mhisto :: (forall y. ((y -> c) -> (y -> f y) -> f y -> c)) -> Fix f -> c
 mhisto ψ = mh where mh = ψ mh unFix . unFix
 
diff --git a/src/Control/Recursion/GHC.hs b/src/Control/Recursion/GHC.hs
--- a/src/Control/Recursion/GHC.hs
+++ b/src/Control/Recursion/GHC.hs
@@ -17,19 +17,19 @@
            => (forall a. Base s (f a) -> f (Base t a))
            -> s
            -> f t
-transverse = cata . (fmap embed .)
+transverse η = cata (fmap embed . η)
 
 cotransverse :: (Recursive s, Corecursive t, Functor f)
              => (forall a. f (Base s a) -> Base t (f a))
              -> f s
              -> t
-cotransverse = ana . (. fmap project)
+cotransverse η = ana (η . fmap project)
 
 hoist :: (Recursive s, Corecursive t)
       => (forall a. Base s a -> Base t a)
       -> s
       -> t
-hoist = cata . (embed .)
+hoist η = cata (embed . η)
 {-# NOINLINE [0] hoist #-}
 
 hoistMu :: (forall a. f a -> g a) -> Mu f -> Mu g