diff --git a/Control/Categorical/Functor.hs b/Control/Categorical/Functor.hs
new file mode 100644
--- /dev/null
+++ b/Control/Categorical/Functor.hs
@@ -0,0 +1,102 @@
+{-# LANGUAGE RankNTypes,
+             GADTs #-}
+
+module Control.Categorical.Functor where
+
+import Control.Category.Dual
+import Control.Category.Groupoid
+import qualified Data.Functor as Base
+import Data.Functor.Compose
+import Data.Functor.Identity
+import Data.Functor.Const
+import Data.Functor.Product
+import Data.Functor.Sum
+import Data.Morphism.Iso
+
+class (Category s, Category t) => Functor (s :: α -> α -> *) (t :: β -> β -> *) (f :: α -> β) where
+    map :: s a b -> t (f a) (f b)
+
+type EndoFunctor s f = Functor s s f
+
+infixl 4 <$>
+(<$>) :: Functor s (->) f => s a b -> f a -> f b
+(<$>) = map
+
+newtype NT s f g = NT { nt :: ∀ a . s (f a) (g a) }
+  deriving (Typeable)
+
+instance Category s => Category (NT s) where
+    id = NT id
+    NT f . NT g = NT (f . g)
+
+instance Groupoid s => Groupoid (NT s) where
+    invert (NT f) = NT (invert f)
+
+instance Base.Functor f => Functor (->) (->) f where map = Base.fmap
+
+instance Category t => Functor (:~:) t f where map Refl = id
+
+instance Functor s (->) f => Functor (NT s) (NT (->)) (Compose f) where
+    map (NT f) = NT (\ (Compose x) -> Compose (f <$> x))
+
+instance Functor (NT (->)) (NT (NT (->))) Compose where
+    map (NT f) = NT (NT (\ (Compose x) -> Compose (f x)))
+
+instance (Functor s (->) f, Functor s (->) g) => Functor s (->) (Sum f g) where
+    map f (InL x) = InL (f <$> x)
+    map f (InR y) = InR (f <$> y)
+
+instance Functor (NT (->)) (NT (->)) (Sum f) where
+    map (NT f) = NT (\ case InL x -> InL x
+                            InR y -> InR (f y))
+
+instance Functor (NT (->)) (NT (NT (->))) Sum where
+    map (NT f) = NT (NT (\ case InL x -> InL (f x)
+                                InR y -> InR y))
+
+instance (Functor s (->) f, Functor s (->) g) => Functor s (->) (Product f g) where
+    map f (Pair x y) = Pair (f <$> x) (f <$> y)
+
+instance Functor (NT (->)) (NT (->)) (Product f) where
+    map (NT f) = NT (\ (Pair x y) -> Pair x (f y))
+
+instance Functor (NT (->)) (NT (NT (->))) Product where
+    map (NT f) = NT (NT (\ (Pair x y) -> Pair (f x) y))
+
+instance Category s => Functor s (->) (Const a) where
+    map _ (Const a) = Const a
+
+instance Functor (->) (NT (->)) Const where
+    map f = NT (\ (Const a) -> Const (f a))
+
+instance Functor (->) (->) Identity where
+    map f (Identity a) = Identity (f a)
+
+instance Category s => Functor s (->) Proxy where
+    map _ Proxy = Proxy
+
+instance Functor (->) (->) ((,) a) where
+    map f (a, b) = (a, f b)
+
+instance Functor (->) (NT (->)) (,) where
+    map f = NT (\ (a, b) -> (f a, b))
+
+instance Functor (->) (->) (Either a) where
+    map _ (Left a) = Left a
+    map f (Right b) = Right (f b)
+
+instance Functor (->) (NT (->)) Either where
+    map f = NT (\ case Left a -> Left (f a)
+                       Right b -> Right b)
+
+instance Category s => Functor s (->) (s a) where
+    map = (.)
+
+instance Category s => Functor (Dual s) (NT (->)) s where
+    map (Dual f) = NT (. f)
+
+instance Functor s t f => Functor (Iso s) t f where
+    map (Iso f _) = map f
+
+instance Functor s t f => Functor (Iso s) (Dual t) f where
+    map (Iso _ f') = Dual (map f')
diff --git a/LICENSE b/LICENSE
new file mode 100644
--- /dev/null
+++ b/LICENSE
@@ -0,0 +1,30 @@
+Copyright (c) 2017, M Farkas-Dyck
+
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are met:
+
+    * Redistributions of source code must retain the above copyright
+      notice, this list of conditions and the following disclaimer.
+
+    * Redistributions in binary form must reproduce the above
+      copyright notice, this list of conditions and the following
+      disclaimer in the documentation and/or other materials provided
+      with the distribution.
+
+    * Neither the name of M Farkas-Dyck nor the names of other
+      contributors may be used to endorse or promote products derived
+      from this software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
diff --git a/Prelude.hs b/Prelude.hs
new file mode 100644
--- /dev/null
+++ b/Prelude.hs
@@ -0,0 +1,7 @@
+module Prelude (module Control.Category,
+                module Data.Either,
+                module Data.Typeable) where
+
+import Control.Category
+import Data.Either
+import Data.Typeable
diff --git a/Setup.hs b/Setup.hs
new file mode 100644
--- /dev/null
+++ b/Setup.hs
@@ -0,0 +1,2 @@
+import Distribution.Simple
+main = defaultMain
diff --git a/functor.cabal b/functor.cabal
new file mode 100644
--- /dev/null
+++ b/functor.cabal
@@ -0,0 +1,29 @@
+name:                functor
+version:             0.1.0.0
+synopsis:            Functors
+-- description:         
+license:             BSD3
+license-file:        LICENSE
+author:              M Farkas-Dyck
+maintainer:          m.farkasdyck@gmail.com
+-- copyright:           
+category:            Control, Math
+build-type:          Simple
+cabal-version:       >=1.10
+
+library
+  exposed-modules:     Control.Categorical.Functor
+  other-modules:       Prelude
+  -- other-extensions:    
+  build-depends:       base >=4.11 && <4.12
+                     , category >=0.1.1 && <0.2
+  -- hs-source-dirs:      
+  default-language:    Haskell2010
+  default-extensions:  LambdaCase
+                     , UnicodeSyntax
+                     , PolyKinds
+                     , ConstraintKinds
+                     , MultiParamTypeClasses
+                     , FlexibleContexts
+                     , FlexibleInstances
+                     , DeriveDataTypeable