diff --git a/fused-effects-exceptions.cabal b/fused-effects-exceptions.cabal
--- a/fused-effects-exceptions.cabal
+++ b/fused-effects-exceptions.cabal
@@ -1,16 +1,17 @@
+cabal-version:       2.4
+
 name:                fused-effects-exceptions
-version:             0.1.1.0
+version:             0.2.0.0
 synopsis:            Handle exceptions thrown in IO with fused-effects.
 description:         Provides an effect that enables catching exceptions thrown from impure computations such as 'IO'.
-homepage:            https://github.com/patrickt/fused-effects-exceptions#readme
-license:             BSD3
+homepage:            https://github.com/fused-effects/fused-effects-exceptions#readme
+license:             BSD-3-Clause
 license-file:        LICENSE
 author:              Josh Vera
 maintainer:          patrickt@github.com
 copyright:           2019 Josh Vera and Patrick Thomson
-category:            Control.
+category:            Control
 build-type:          Simple
-cabal-version:       >=1.10
 extra-source-files:  README.md
 
 tested-with:         GHC == 8.6.4
@@ -19,10 +20,10 @@
   hs-source-dirs:      src
   default-language:    Haskell2010
   exposed-modules:     Control.Effect.Catch
-  build-depends:       base >= 4.7 && < 5
-                     , fused-effects >= 0.3 && <1
+  build-depends:       base            >= 4.7 && < 5
+                     , fused-effects   ^>= 0.5
                      , safe-exceptions >= 0.1 && <1
-                     , unliftio-core >= 0.1.2 && <1
+                     , unliftio-core   >= 0.1.2 && <1
 
 source-repository head
   type:     git
diff --git a/src/Control/Effect/Catch.hs b/src/Control/Effect/Catch.hs
--- a/src/Control/Effect/Catch.hs
+++ b/src/Control/Effect/Catch.hs
@@ -14,7 +14,6 @@
   , catch
   , catchSync
   , runCatch
-  , withCatch
   , CatchC (..)
   ) where
 
@@ -27,12 +26,12 @@
 import           Control.Monad.IO.Unlift
 
 data Catch m k
-  = forall output e . Exc.Exception e => CatchIO (m output) (e -> m output) (output -> k)
+  = forall output e . Exc.Exception e => CatchIO (m output) (e -> m output) (output -> m k)
 
-deriving instance Functor (Catch m)
+deriving instance Functor m => Functor (Catch m)
 
 instance HFunctor Catch where
-  hmap f (CatchIO go cleanup k) = CatchIO (f go) (f . cleanup) k
+  hmap f (CatchIO go cleanup k) = CatchIO (f go) (f . cleanup) (f . k)
 
 instance Effect Catch where
   handle state handler (CatchIO go cleanup k)
@@ -63,15 +62,15 @@
       else liftIO (Exc.throw e)
 
 -- | Evaluate a 'Catch' effect.
-runCatch :: (forall x . m x -> IO x)
-         -> CatchC m a
-         -> m a
-runCatch handler = runReader (Handler handler) . runCatchC
+unliftCatch :: (forall x . m x -> IO x)
+            -> CatchC m a
+            -> m a
+unliftCatch handler = runReader (Handler handler) . runCatchC
 
 -- | Evaluate a 'Catch' effect, using 'MonadUnliftIO' to infer a correct
 -- unlifting function.
-withCatch :: MonadUnliftIO m => CatchC m a -> m a
-withCatch c = withRunInIO (\f -> runHandler (Handler f) c)
+runCatch :: MonadUnliftIO m => CatchC m a -> m a
+runCatch c = withRunInIO (\f -> runHandler (Handler f) c)
 
 newtype Handler m = Handler (forall x . m x -> IO x)
 
@@ -83,7 +82,7 @@
 
 instance MonadUnliftIO m => MonadUnliftIO (CatchC m) where
   askUnliftIO = CatchC . ReaderC $ \(Handler h) ->
-    withUnliftIO $ \u -> pure (UnliftIO $ \r -> unliftIO u (runCatch h r))
+    withUnliftIO $ \u -> pure (UnliftIO $ \r -> unliftIO u (unliftCatch h r))
 
 instance (Carrier sig m, MonadIO m) => Carrier (Catch :+: sig) (CatchC m) where
   eff (L (CatchIO act cleanup k)) = do