diff --git a/Control/Category/Cartesian.hs b/Control/Category/Cartesian.hs
--- a/Control/Category/Cartesian.hs
+++ b/Control/Category/Cartesian.hs
@@ -46,16 +46,16 @@
 > fst, snd, diag 
 > fst, snd, (&&&)
 -}
-class ( Associative (~>) (Product (~>))
-      , Disassociative (~>) (Product (~>))
-      , Symmetric (~>) (Product (~>))
-      , Braided (~>) (Product (~>))
-      ) => PreCartesian (~>) where
-    type Product (~>) :: * -> * -> *
-    fst :: Product (~>) a b ~> a
-    snd :: Product (~>) a b ~> b
-    diag :: a ~> Product (~>) a a
-    (&&&) :: (a ~> b) -> (a ~> c) -> a ~> Product (~>) b c
+class ( Associative k (Product k)
+      , Disassociative k (Product k)
+      , Symmetric k (Product k)
+      , Braided k (Product k)
+      ) => PreCartesian k where
+    type Product k :: * -> * -> *
+    fst :: Product k a b `k` a
+    snd :: Product k a b `k` b
+    diag :: a `k` Product k a a
+    (&&&) :: (a `k` b) -> (a `k` c) -> a `k` Product k b c
 
     diag = id &&& id
     f &&& g = bimap f g . diag
@@ -76,45 +76,45 @@
     (f &&& g) a = (f a, g a)
 
 -- alias
-class ( Monoidal (~>) (Product (~>))
-      , PreCartesian (~>)
-      ) => Cartesian (~>)
-instance ( Monoidal (~>) (Product (~>))
-         , PreCartesian (~>)
-         ) => Cartesian (~>)
+class ( Monoidal k (Product k)
+      , PreCartesian k
+      ) => Cartesian k
+instance ( Monoidal k (Product k)
+         , PreCartesian k
+         ) => Cartesian k
 
 -- | free construction of 'Bifunctor' for the product 'Bifunctor' @Product k@ if @(&&&)@ is known
-bimapProduct :: (PreCartesian (~>), (<*>) ~ Product (~>)) => (a ~> c) -> (b ~> d) -> (a <*> b) ~> (c <*> d)
+bimapProduct :: (PreCartesian k, (<*>) ~ Product k) => (a `k` c) -> (b `k` d) -> (a <*> b) `k` (c <*> d)
 bimapProduct f g = (f . fst) &&& (g . snd)
     
 -- | free construction of 'Braided' for the product 'Bifunctor' @Product k@
--- braidProduct :: (PreCartesian (~>), Product (~>) ~ (<*>))  => a <*> b ~> b <*> a
-braidProduct :: (PreCartesian (~>)) => Product (~>) a b ~> Product (~>) b a
+-- braidProduct :: (PreCartesian k, Product k ~ (<*>))  => a <*> b ~> b <*> a
+braidProduct :: (PreCartesian k) => Product k a b `k` Product k b a
 braidProduct = snd &&& fst
 
 -- | free construction of 'Associative' for the product 'Bifunctor' @Product k@
--- associateProduct :: (PreCartesian (~>), (<*>) ~ Product (~>))  => (a <*> b) <*> c ~> (a <*> (b <*> c))
-associateProduct :: (PreCartesian (~>)) => Product (~>) (Product (~>) a b) c ~> Product (~>) a (Product (~>) b c)
+-- associateProduct :: (PreCartesian k, (<*>) ~ Product k)  => (a <*> b) <*> c ~> (a <*> (b <*> c))
+associateProduct :: (PreCartesian k) => Product k (Product k a b) c `k` Product k a (Product k b c)
 associateProduct = (fst . fst) &&& first snd
 
 -- | free construction of 'Disassociative' for the product 'Bifunctor' @Product k@
--- disassociateProduct:: (PreCartesian (~>),  (<*>) ~ Product (~>)) => a <*> (b <*> c) ~> (a <*> b) <*> c
-disassociateProduct:: (PreCartesian (~>)) => Product (~>) a (Product (~>) b c) ~> Product (~>) (Product (~>) a b) c
+-- disassociateProduct:: (PreCartesian k,  (<*>) ~ Product k) => a <*> (b <*> c) ~> (a <*> b) <*> c
+disassociateProduct:: (PreCartesian k) => Product k a (Product k b c) `k` Product k (Product k a b) c
 disassociateProduct= braid . second braid . associateProduct . first braid . braid 
 
 -- * Co-PreCartesian categories
 
--- a category that has finite coproducts, wea(~>)ened the same way as PreCartesian above was wea(~>)ened
-class ( Associative (~>) (Sum (~>))
-      , Disassociative (~>) (Sum (~>))
-      , Symmetric (~>) (Product (~>))
-      , Braided (~>) (Sum (~>))
-      ) => PreCoCartesian (~>) where
-    type Sum (~>) :: * -> * -> *
-    inl :: a ~> Sum (~>) a b
-    inr :: b ~> Sum (~>) a b
-    codiag :: Sum (~>) a a ~> a
-    (|||) :: (a ~> c) -> (b ~> c) -> Sum (~>) a b ~> c
+-- a category that has finite coproducts, weakened the same way as PreCartesian above was weakened
+class ( Associative k (Sum k)
+      , Disassociative k (Sum k)
+      , Symmetric k (Product k)
+      , Braided k (Sum k)
+      ) => PreCoCartesian k where
+    type Sum k :: * -> * -> *
+    inl :: a `k` Sum k a b
+    inr :: b `k` Sum k a b
+    codiag :: Sum k a a `k` a
+    (|||) :: (a `k` c) -> (b `k` c) -> Sum k a b `k` c
 
     codiag = id ||| id
     f ||| g = codiag . bimap f g
@@ -135,29 +135,29 @@
     (f ||| _) (Left a) = f a 
     (_ ||| g) (Right a) = g a
 
--- | free construction of 'Bifunctor' for the coproduct 'Bifunctor' @Sum (~>)@ if @(|||)@ is known
-bimapSum :: (PreCoCartesian (~>), Sum (~>) ~ (+)) => (a ~> c) -> (b ~> d) -> (a + b) ~> (c + d)
+-- | free construction of 'Bifunctor' for the coproduct 'Bifunctor' @Sum k@ if @(|||)@ is known
+bimapSum :: (PreCoCartesian k, Sum k ~ (+)) => (a `k` c) -> (b `k` d) -> (a + b) `k` (c + d)
 bimapSum f g = (inl . f) ||| (inr . g)
 
--- | free construction of 'Braided' for the coproduct 'Bifunctor' @Sum (~>)@
-braidSum :: (PreCoCartesian (~>), (+) ~ Sum (~>)) => (a + b) ~> (b + a)
+-- | free construction of 'Braided' for the coproduct 'Bifunctor' @Sum k@
+braidSum :: (PreCoCartesian k, (+) ~ Sum k) => (a + b) `k` (b + a)
 braidSum = inr ||| inl
 
--- | free construction of 'Associative' for the coproduct 'Bifunctor' @Sum (~>)@
--- associateSum :: (PreCoCartesian (~>), (+) ~ Sum (~>)) => ((a + b) + c) ~> (a + (b + c))
-associateSum :: (PreCoCartesian (~>)) => Sum (~>) (Sum (~>) a b) c ~> Sum (~>) a (Sum (~>) b c)
+-- | free construction of 'Associative' for the coproduct 'Bifunctor' @Sum k@
+-- associateSum :: (PreCoCartesian k, (+) ~ Sum k) => ((a + b) + c) ~> (a + (b + c))
+associateSum :: (PreCoCartesian k) => Sum k (Sum k a b) c `k` Sum k a (Sum k b c)
 associateSum = braid . first braid . disassociateSum . second braid . braid
 
--- | free construction of 'Disassociative' for the coproduct 'Bifunctor' @Sum (~>)@
--- disassociateSum :: (PreCoCartesian (~>), (+) ~ Sum (~>)) => (a + (b + c)) ~> ((a + b) + c)
-disassociateSum :: (PreCoCartesian (~>)) => Sum (~>) a (Sum (~>) b c) ~> Sum (~>) (Sum (~>) a b) c
+-- | free construction of 'Disassociative' for the coproduct 'Bifunctor' @Sum k@
+-- disassociateSum :: (PreCoCartesian k, (+) ~ Sum k) => (a + (b + c)) ~> ((a + b) + c)
+disassociateSum :: (PreCoCartesian k) => Sum k a (Sum k b c) `k` Sum k (Sum k a b) c
 disassociateSum = (inl . inl) ||| first inr
 
 class 
-    ( Comonoidal (~>) (Sum (~>))
-    , PreCoCartesian (~>)
-    ) => CoCartesian (~>)
+    ( Comonoidal k (Sum k)
+    , PreCoCartesian k
+    ) => CoCartesian k
 instance 
-    ( Comonoidal (~>) (Sum (~>))
-    , PreCoCartesian (~>)
-    ) => CoCartesian (~>)
+    ( Comonoidal k (Sum k)
+    , PreCoCartesian k
+    ) => CoCartesian k
diff --git a/Control/Category/Discrete.hs b/Control/Category/Discrete.hs
--- a/Control/Category/Discrete.hs
+++ b/Control/Category/Discrete.hs
@@ -34,7 +34,7 @@
 liftDiscrete Refl = Refl
 
 -- | Lower the proof that a ~ b to an arbitrary category.
-cast :: Category (~>) => Discrete a b -> (a ~> b)
+cast :: Category k => Discrete a b -> k a b
 cast Refl = id
 
 -- | 
diff --git a/Control/Category/Distributive.hs b/Control/Category/Distributive.hs
--- a/Control/Category/Distributive.hs
+++ b/Control/Category/Distributive.hs
@@ -22,28 +22,30 @@
 import Control.Category
 import Control.Category.Cartesian
 
--- | the canonical factoring morphism 
+-- | The canonical factoring morphism.
 -- 
--- > factor :: ( PreCartesian (~>)
--- >         , (*) ~ Product (~>)
--- >         , PreCoCartesian (~>)
--- >         , (+) ~ Sum (~>) 
--- >         ) => ((a * b) + (a * c)) ~> (a * (b + c))
+-- > factor :: ( PreCartesian k
+-- >         , (*) ~ Product k
+-- >         , PreCoCartesian k
+-- >         , (+) ~ Sum k 
+-- >         ) => ((a * b) + (a * c)) `k` (a * (b + c))
 
-factor :: ( PreCartesian (~>)
-          , PreCoCartesian (~>)
-          ) => Sum (~>) (Product (~>) a b) (Product (~>) a c) ~> Product (~>) a (Sum (~>) b c)
+factor :: ( PreCartesian k
+          , PreCoCartesian k
+          ) => Sum k (Product k a b) (Product k a c) `k` Product k a (Sum k b c)
 factor = second inl ||| second inr
 
 -- | A category in which 'factor' is an isomorphism
--- > class ( PreCartesian (~>) 
--- >       , (*) ~ Product (~>)
--- >       , PreCoCartesian (~>)
--- >       , (+) ~ Sum (~>) 
--- >       ) => Distributive (~>) where
-class (PreCartesian (~>), PreCoCartesian (~>)) => Distributive (~>) where
-    distribute :: Product (~>) a (Sum (~>) b c) ~> Sum (~>) (Product (~>) a b) (Product (~>) a c)
+--
+-- > class ( PreCartesian k 
+-- >       , (*) ~ Product k
+-- >       , PreCoCartesian k
+-- >       , (+) ~ Sum k 
+-- >       ) => Distributive k where
 
+class (PreCartesian k, PreCoCartesian k) => Distributive k where
+    distribute :: Product k a (Sum k b c) `k` Sum k (Product k a b) (Product k a c)
+
 instance Distributive (->) where
     distribute (a, Left b) = Left (a,b)
     distribute (a, Right c) = Right (a,c)
@@ -51,4 +53,4 @@
 {-# RULES
 "factor . distribute" factor . distribute = id
 "distribute . factor" distribute . factor = id
- #-}
+  #-}
diff --git a/categories.cabal b/categories.cabal
--- a/categories.cabal
+++ b/categories.cabal
@@ -1,6 +1,6 @@
 name:          categories
 category:      Control
-version:       0.54.0
+version:       0.54.1
 license:       BSD3
 cabal-version: >= 1.2
 license-file:  LICENSE