diff --git a/Control/Category/Product.hs b/Control/Category/Product.hs
new file mode 100644
--- /dev/null
+++ b/Control/Category/Product.hs
@@ -0,0 +1,19 @@
+module Control.Category.Product ((:×:) (..)) where
+
+import Control.Category
+import Control.Category.Groupoid
+import Data.Type.Equality
+
+data ((s :: αₛ -> αₛ -> *) :×: (t :: αₜ -> αₜ -> *)) :: (αₛ, αₜ) -> (αₛ, αₜ) -> * where
+    (:×:) :: s aₛ bₛ -> t aₜ bₜ -> (s :×: t) '(aₛ, aₜ) '(bₛ, bₜ)
+
+instance (Category s, Category t) => Category (s :×: t) where
+    id :: ∀ a . (s :×: t) a a
+    id = pair `gcastWith` (id :×: id) where pair = pair :: a :~: '(Fst a, Snd a)
+    (fₛ :×: fₜ) . (gₛ :×: gₜ) = (fₛ . gₛ) :×: (fₜ . gₜ)
+
+type family Fst a where Fst '(a, b) = a
+type family Snd a where Snd '(a, b) = b
+
+instance (Groupoid s, Groupoid t) => Groupoid (s :×: t) where
+    invert (f :×: g) = invert f :×: invert g
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 +1,3 @@
+module Prelude (module Control.Category) where
+
+import Control.Category
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/product.cabal b/product.cabal
new file mode 100644
--- /dev/null
+++ b/product.cabal
@@ -0,0 +1,29 @@
+name:                product
+version:             0.1.0.0
+synopsis:            Product category
+-- description:         
+license:             BSD3
+license-file:        LICENSE
+author:              M Farkas-Dyck
+maintainer:          m.farkasdyck@gmail.com
+-- copyright:           
+category:            Math
+build-type:          Simple
+cabal-version:       >=1.10
+
+library
+  exposed-modules:     Control.Category.Product
+  other-modules:       Prelude
+  -- other-extensions:    
+  build-depends:       base >=4.10 && <5
+                     , category
+  -- hs-source-dirs:      
+  default-language:    Haskell2010
+  default-extensions:  UnicodeSyntax
+                     , TypeOperators
+                     , ScopedTypeVariables
+                     , InstanceSigs
+                     , PolyKinds
+                     , DataKinds
+                     , TypeFamilies
+                     , GADTs