diff --git a/Data/Profunctor/Cayley.idr b/Data/Profunctor/Cayley.idr
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+module Data.Profunctor.Cayley
+
+import Data.Profunctor
+import Data.Profunctor.Costrong
+import Data.Profunctor.Traversing
+import Data.Profunctor.Mapping
+import Data.Profunctor.Sieve
+
+%default total
+
+
+public export
+record Cayley {0 k1,k2,k3 : Type} f (p : k1 -> k2 -> k3) a b where
+  constructor MkCayley
+  runCayley : f (p a b)
+
+
+export
+Functor f => Profunctor p => Profunctor (Cayley f p) where
+  dimap f g (MkCayley p) = MkCayley (dimap f g <$> p)
+  lmap f (MkCayley p) = MkCayley (lmap f <$> p)
+  rmap g (MkCayley p) = MkCayley (rmap g <$> p)
+
+export
+Functor f => ProfunctorFunctor (Cayley f) where
+  promap f (MkCayley p) = MkCayley (map f p)
+
+export
+Monad m => ProfunctorMonad (Cayley m) where
+  propure = MkCayley . pure
+  projoin (MkCayley p) = MkCayley $ p >>= runCayley
+
+export
+Functor f => GenStrong ten p => GenStrong ten (Cayley f p) where
+  strongl (MkCayley p) = MkCayley (strongl {ten} <$> p)
+  strongr (MkCayley p) = MkCayley (strongr {ten} <$> p)
+
+export
+Functor f => GenCostrong ten p => GenCostrong ten (Cayley f p) where
+  costrongl (MkCayley p) = MkCayley (costrongl {ten} <$> p)
+  costrongr (MkCayley p) = MkCayley (costrongr {ten} <$> p)
+
+export
+Functor f => Closed p => Closed (Cayley f p) where
+  closed (MkCayley p) = MkCayley (closed <$> p)
+
+export
+Functor f => Traversing p => Traversing (Cayley f p) where
+  traverse' (MkCayley p) = MkCayley (traverse' <$> p)
+  wander f (MkCayley p) = MkCayley (wander f <$> p)
+
+export
+Functor f => Mapping p => Mapping (Cayley f p) where
+  map' (MkCayley p) = MkCayley (map' <$> p)
+  roam f (MkCayley p) = MkCayley (roam f <$> p)
+
+
+export
+mapCayley : (forall x. f x -> g x) -> Cayley f p a b -> Cayley g p a b
+mapCayley f (MkCayley p) = MkCayley (f p)