diff --git a/linear-base.cabal b/linear-base.cabal
index 3771d360..712e1b9e 100644
--- a/linear-base.cabal
+++ b/linear-base.cabal
@@ -1,5 +1,5 @@
 name: linear-base
-version: 0.1.1
+version: 0.1.2
 cabal-version: >=1.10
 homepage: https://github.com/tweag/linear-base#README
 license: MIT
@@ -22,6 +22,8 @@ library
   hs-source-dirs: src
   exposed-modules:
     Control.Monad.IO.Class.Linear
+    Control.Arrow.Linear
+    Control.Category.Linear
     Control.Functor.Linear
     Control.Functor.Linear.Internal.Class
     Control.Functor.Linear.Internal.Instances
diff --git a/src/Control/Arrow/Linear.hs b/src/Control/Arrow/Linear.hs
new file mode 100644
index 00000000..52661419
--- /dev/null
+++ b/src/Control/Arrow/Linear.hs
@@ -0,0 +1,128 @@
+{-# LANGUAGE FlexibleInstances #-}
+{-# LANGUAGE LinearTypes #-}
+{-# LANGUAGE NoImplicitPrelude #-}
+
+module Control.Arrow.Linear (
+  -- | Arrows
+  Arrow(..),
+  Kleisli(..),
+  -- | Derived function
+  (^>>), (>>^), (>>>), returnA,
+  -- | Right-to-left variants
+  (<<^), (^<<), (<<<),
+  -- | Arrow Application
+  ArrowApply(..),
+  -- | Feedback
+  ArrowLoop(..)
+
+) where
+
+import Control.Category.Linear ( (<<<), (>>>), Category(..) )
+import Control.Functor.Linear as Control
+import Data.Profunctor.Kleisli.Linear (Kleisli(..))
+import Data.Unrestricted.Linear ( Dupable(dup2) )
+import GHC.Exts(FUN)
+import GHC.Types (Multiplicity(One))
+
+-- | A linear Arrow
+class Category a => Arrow a where
+    -- | Lift function to an arrow
+    arr    :: (b %1 -> c) %1 -> a b c
+
+    -- | Send the first component of the input through the argument
+    --   arrow, and copy the rest unchanged to the output.
+    first  :: a b c %1 -> a (b,d) (c,d)
+    first = (*** id)
+
+    -- | A mirror image of 'first'.
+    --
+    --   The default definition may be overridden with a more efficient
+    --   version if desired.
+    second :: a b c %1 -> a (d,b) (d,c)
+    second = (id ***)
+
+    -- | Split the input between the two argument arrows and combine
+    --   their output.  Note that this is in general not a functor.
+    --
+    --   The default definition may be overridden with a more efficient
+    --   version if desired.
+    (***)  :: a b c %1 -> a b' c' %1 -> a (b,b') (c,c')
+    f *** g = first f >>> arr swap >>> first g >>> arr swap
+      where
+        swap :: (x,y) %1 -> (y,x)
+        swap (x,y) = (y,x)
+    infixr 3 ***
+
+    -- | Fanout: send the input to both argument arrows and combine
+    --   their output.
+    --
+    --   This requires the input to be `Dupable`
+    (&&&) :: (Dupable b) => a b c %1 -> a b c' %1 -> a b (c,c')
+    f &&& g = arr dup2 >>> (f *** g)
+
+class Arrow a => ArrowLoop a where
+    loop :: a (b,d) (c,d) %1 -> a b c
+
+
+-- | Some arrows allow application of arrow inputs to other inputs.
+-- Instances should satisfy the following laws:
+--
+--  * @'first' ('arr' (\\x -> 'arr' (\\y -> (x,y)))) >>> 'app' = 'id'@
+--
+--  * @'first' ('arr' (g >>>)) >>> 'app' = 'second' g >>> 'app'@
+--
+--  * @'first' ('arr' (>>> h)) >>> 'app' = 'app' >>> h@
+--
+-- Such arrows are equivalent to monads (see 'ArrowMonad').
+class Arrow a => ArrowApply a where
+    app :: a (a b c, b) c
+
+
+-- Need category instance for (FUN 'Many)
+returnA :: Arrow a => a b b
+returnA = arr id
+
+-- Derived combinators
+
+
+-- | Pre-composition with a pure function.
+(^>>) :: Arrow a => (b %1 -> c) %1 -> a c d %1 -> a b d
+f ^>> a = arr f >>> a
+infixr 1 ^>>
+
+-- | Post-composition with a pure function.
+(>>^) :: Arrow a => a b c %1 -> (c %1 -> d) %1 -> a b d
+a >>^ f = a >>> arr f
+infixr 1 >>^
+
+-- Right to left variants
+
+-- | Pre-composition with a pure function (right-to-left variant).
+(<<^) :: Arrow a => a c d %1 -> (b %1 -> c) %1 -> a b d
+a <<^ f = a <<< arr f
+infixr 1 <<^
+
+-- | Post-composition with a pure function (right-to-left variant).
+(^<<) :: Arrow a => (c %1 -> d) %1 -> a b c %1 -> a b d
+f ^<< a = arr f <<< a
+infixr 1 ^<<
+
+
+instance Arrow (FUN 'One) where
+  arr f = f
+  (f *** g) (x,y) = (f x, g y)
+  -- | NOTE: `~(x,y)` is the NonLinear pattern match
+
+
+instance ArrowApply (FUN 'One) where
+  app (f,x) = f x
+
+
+instance Monad m => Arrow (Kleisli m) where
+    arr f = Kleisli (return . f)
+    first (Kleisli f) = Kleisli (\ (b,d) -> f b >>= \c -> return (c,d))
+    second (Kleisli f) = Kleisli (\ (d,b) -> f b >>= \c -> return (d,c))
+
+
+instance Monad m => ArrowApply (Kleisli m) where
+    app = Kleisli (\(Kleisli f, x) -> f x)
diff --git a/src/Control/Category/Linear.hs b/src/Control/Category/Linear.hs
new file mode 100644
index 00000000..a7c0f3e4
--- /dev/null
+++ b/src/Control/Category/Linear.hs
@@ -0,0 +1,37 @@
+{-# LANGUAGE FlexibleInstances #-}
+{-# LANGUAGE LinearTypes #-}
+{-# LANGUAGE NoImplicitPrelude #-}
+
+module Control.Category.Linear where
+
+import qualified Prelude.Linear
+import GHC.Exts(FUN)
+import GHC.Types (Multiplicity(One))
+import Control.Functor.Linear as Control
+import Data.Profunctor.Kleisli.Linear (Kleisli(..))
+
+class Category cat where
+  id :: cat a a
+  (.) :: cat b c %1 -> cat a b %1 -> cat a c
+  infixr 9 .
+
+-- | Left-to-right composition
+(>>>) :: Category cat => cat a b %1 -> cat b c %1 -> cat a c
+f >>> g = (Control.Category.Linear..) g f
+infixr 1 >>>
+{-# INLINE (>>>) #-}
+
+-- | Right-to-left composition
+(<<<) :: Category cat => cat b c %1 -> cat a b %1 -> cat a c
+(<<<) = (Control.Category.Linear..)
+infixr 1 <<<
+
+
+instance Category (FUN 'One) where
+  id = Prelude.Linear.id
+  (.) = (Prelude.Linear..)
+
+
+instance Monad m => Category (Kleisli m) where
+    id = Kleisli return
+    (Kleisli f) . (Kleisli g) = Kleisli (\b -> g b >>= f)