diff --git a/CHANGELOG.md b/CHANGELOG.md
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,5 +1,13 @@
 # recursion
 
+## 1.2.1.0
+
+* Add `chema`, `scolio`, and `dendro`
+
+## 1.2.0.1
+
+* Patch export of `cata`/`ana`
+
 ## 1.2.0.0
 
 * Remove `chema`
diff --git a/recursion.cabal b/recursion.cabal
--- a/recursion.cabal
+++ b/recursion.cabal
@@ -1,6 +1,6 @@
 cabal-version: 1.18
 name: recursion
-version: 1.2.0.1
+version: 1.2.1.0
 license: BSD3
 license-file: LICENSE
 copyright: Copyright: (c) 2018 Vanessa McHale
diff --git a/src/Control/Recursion.hs b/src/Control/Recursion.hs
--- a/src/Control/Recursion.hs
+++ b/src/Control/Recursion.hs
@@ -38,9 +38,15 @@
     , cataM
     , anaM
     , hyloM
+    -- * Mutual recursion
+    , scolio
+    , dendro
+    , chema
     -- * Helper functions
     , lambek
     , colambek
+    , hoist
+    , refix
     ) where
 
 import           Control.Arrow       ((&&&))
@@ -62,6 +68,12 @@
 
     embed :: Base t t -> t
 
+-- | A map of \\( F \\)-algebras (pseudoprism)
+type Trans s a = forall f. Functor f => (f a -> a) -> f s -> s
+
+-- | A map of \\( F \\)-coalgebras
+type Lens s a = forall f. Functor f => (a -> f a) -> s -> f s
+
 data ListF a b = Cons a b
                | Nil
                deriving (Functor)
@@ -77,6 +89,8 @@
 
 type instance Base (Fix f) = f
 
+type instance Base (Fix f) = f
+
 type instance Base (Mu f) = f
 
 type instance Base (Nu f) = f
@@ -123,6 +137,12 @@
     embed (NonEmptyF x Nothing)   = x :| []
     embed (NonEmptyF x (Just xs)) = x :| toList xs
 
+instance Functor f => Recursive (Fix f) where
+    project = unFix
+
+instance Functor f => Corecursive (Fix f) where
+    embed = Fix
+
 -- | Catamorphism. Folds a structure. (see [here](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.41.125&rep=rep1&type=pdf))
 cata :: (Recursive t) => (Base t a -> a) -> t -> a
 cata f = c where c = f . fmap c . project
@@ -226,3 +246,41 @@
 -- | Apomorphism. Compare 'micro'.
 apo :: (Corecursive t) => (a -> Base t (Either t a)) -> a -> t
 apo g = a where a = embed . fmap (either id a) . g
+
+hoist :: (Recursive s, Corecursive t)
+      => (forall a. Base s a -> Base t a)
+      -> s
+      -> t
+hoist = cata . (embed .)
+
+refix :: (Recursive s, Corecursive t, Base s ~ Base t) => s -> t
+refix = cata embed
+
+-- | Entangle two hylomorphisms.
+scolio :: (Functor g)
+    => ((f b -> b) -> Trans b b) -- ^ A pseudoprism parametric in an \\( F \\)-algebra that allows @b@ to inspect itself.
+    -> ((a -> f a) -> Lens a a) -- ^ A lens parametric in an \\( F \\)-coalgebra that allows @b@ to inspect itself.
+    -> (g b -> b) -- ^ A @g@-algebra
+    -> (a -> g a) -- ^ A @g@-coalgebra
+    -> (f b -> b) -- ^ An @f@-algebra
+    -> (a -> f a) -- ^ An @f@-coalgebra
+    -> a -> b
+scolio p l alg coalg alg' coalg' = hylo (p alg' alg) (l coalg' coalg)
+-- TODO: figure out rewrite rules
+-- also a more flexible approach would be good.
+
+-- Entangle two anamorphisms.
+chema :: (Corecursive t')
+    => ((a -> f a) -> Lens b b) -- ^ A lens parametric in an \\( F \\)-coalgebra that allows @b@ to inspect itself.
+    -> (a -> f a) -- ^ A @(Base t)@-coalgebra
+    -> (b -> Base t' b) -- ^ A @(Base t')@-coalgebra
+    -> b -> t'
+chema = (ana .*)
+
+-- | A dendromorphism entangles two catamorphisms
+dendro :: (Recursive t')
+    => ((f a -> a) -> Trans b b) -- ^ A pseudoprism parametric in an \\(F \\)-algebra that allows @b@ to inspect itself.
+    -> (f a -> a) -- ^ A @(Base t)@-algebra
+    -> (Base t' b -> b) -- ^ A @(Base t')@-algebra
+    -> t' -> b
+dendro = (cata .*)