diff --git a/Data/Eq/Type.hs b/Data/Eq/Type.hs
--- a/Data/Eq/Type.hs
+++ b/Data/Eq/Type.hs
@@ -39,6 +39,7 @@
 import Prelude ()
 import Control.Category 
 import Data.Semigroupoid
+import Data.Groupoid
 
 infixl 4 :=
 
@@ -62,6 +63,9 @@
 
 instance Semigroupoid (:=) where
   o = subst
+
+instance Groupoid (:=) where
+  inv = symm
 
 -- | Equality is transitive
 trans :: a := b -> b := c -> a := c
diff --git a/eq.cabal b/eq.cabal
--- a/eq.cabal
+++ b/eq.cabal
@@ -1,6 +1,6 @@
 name:          eq
 category:      Type System
-version:       0.3.3.1
+version:       0.3.4
 license:       BSD3
 cabal-version: >= 1.6
 license-file:  LICENSE
@@ -25,7 +25,8 @@
 
   build-depends: 
     base >= 4 && < 5,
-    semigroupoids >= 1.2.2 && < 1.3.0
+    semigroupoids >= 1.2.2 && < 1.3.0,
+    groupoids >= 0.1 && < 0.2
 
   exposed-modules:
     Data.Eq.Type