diff --git a/src/Test/Invariant.hs b/src/Test/Invariant.hs
--- a/src/Test/Invariant.hs
+++ b/src/Test/Invariant.hs
@@ -9,7 +9,7 @@
 -- definitions of laws.
 --
 -- > f(x) == g(x)
--- > f <=> f . f
+-- > f <=> g
 (<=>) :: Eq b => (a -> b) -> (a -> b) -> a -> Bool
 (f <=> g) x = f x == g x
 
@@ -206,6 +206,15 @@
 invariatesOver :: Eq b => (a -> b) -> (a -> a) -> a -> Bool
 f `invariatesOver` g = f . g <=> f
 
+-- | Checks whether a binary function is fixed by an argument.
+--
+-- f x y == const a y
+--
+-- >>> quickCheck $ (*) `fixedBy` 0
+-- +++ OK, passed 100 tests.
+fixedBy :: Eq c => (a -> b -> c) -> a -> b -> b -> Bool
+(f `fixedBy` x) y z = f x y == f x z
+
 -- | Checks whether a function is invariant over an other function.
 --
 -- >>> quickCheck $ length <~~ reverse
@@ -222,7 +231,7 @@
 (@~>) :: Eq a => (b -> a) -> (a -> b) -> a -> Bool
 f @~> g = f . g <=> id
 
--- | Checks whether two functions commutate.
+-- | Checks whether a function is an endomorphism in relation to a unary operator.
 --
 -- > f(g(x)) = g(f(x))
 --
@@ -230,3 +239,19 @@
 -- +++ OK, passed 100 tests.
 (<?>) :: Eq a => (a -> a) -> (a -> a) -> a -> Bool
 f <?> g = f . g <=> g . f
+
+-- | Checks whether a function is an endomorphism in relation to a binary operator.
+--
+-- > f(g(x,y)) = g(f(x),f(y))
+--
+-- >>> quickCheck $ (^2) <??> (*)
+-- +++ OK, passed 100 tests.
+(<??>) :: Eq a => (a -> a) -> (a -> a -> a) -> a -> a -> Bool
+(f <??> g) x y = f (x `g` y) == f x `g` f y
+
+-- | Checks whether a function is an endomorphism in relation to a ternary operator.
+--
+-- > f(g(x,y,z)) = g(f(x),f(y),f(z))
+--
+(<???>) :: Eq a => (a -> a) -> (a -> a -> a -> a) -> a -> a -> a -> Bool
+(f <???> g) x y z = f (g x y z) == g (f x) (f y) (f z)
diff --git a/test-invariant.cabal b/test-invariant.cabal
--- a/test-invariant.cabal
+++ b/test-invariant.cabal
@@ -1,5 +1,5 @@
 name:                test-invariant
-version:             0.4.4.0
+version:             0.4.5.0
 synopsis:            Provide common invariants to be checked with QuickCheck
 
 description: test-invariant is a library for providing common invariants of