diff --git a/Control/Categorical/Functor.hs b/Control/Categorical/Functor.hs
deleted file mode 100644
--- a/Control/Categorical/Functor.hs
+++ /dev/null
@@ -1,94 +0,0 @@
-{-# LANGUAGE RankNTypes #-}
-
-module Control.Categorical.Functor where
-
-import Control.Category.Dual
-import Control.Category.Groupoid
-import qualified Data.Functor as Base
-import Data.Functor.Compose
-import Data.Functor.Identity
-import Data.Functor.Const
-import Data.Functor.Product
-import Data.Functor.Sum
-import Data.Proxy
-
-class (Category s, Category t) => Functor (s :: α -> α -> *) (t :: β -> β -> *) (f :: α -> β) where
-    map :: s a b -> t (f a) (f b)
-
-{-# DEPRECATED EndoFunctor "Use Endofunctor" #-}
-type EndoFunctor s = Functor s s
-type Endofunctor s = Functor s s
-
-infixl 4 <$>
-(<$>) :: Functor s (->) f => s a b -> f a -> f b
-(<$>) = map
-
-newtype NT s f g = NT { nt :: ∀ a . s (f a) (g a) }
-
-instance Category s => Category (NT s) where
-    id = NT id
-    NT f . NT g = NT (f . g)
-
-instance Groupoid s => Groupoid (NT s) where
-    invert (NT f) = NT (invert f)
-
-instance {-# INCOHERENT #-} Base.Functor f => Functor (->) (->) f where map = Base.fmap
-
-instance Functor s (->) f => Functor (NT s) (NT (->)) (Compose f) where
-    map (NT f) = NT (\ (Compose x) -> Compose (f <$> x))
-
-instance Functor (NT (->)) (NT (NT (->))) Compose where
-    map (NT f) = NT (NT (\ (Compose x) -> Compose (f x)))
-
-instance (Functor s (->) f, Functor s (->) g) => Functor s (->) (Sum f g) where
-    map f (InL x) = InL (f <$> x)
-    map f (InR y) = InR (f <$> y)
-
-instance Functor (NT (->)) (NT (->)) (Sum f) where
-    map (NT f) = NT (\ case InL x -> InL x
-                            InR y -> InR (f y))
-
-instance Functor (NT (->)) (NT (NT (->))) Sum where
-    map (NT f) = NT (NT (\ case InL x -> InL (f x)
-                                InR y -> InR y))
-
-instance (Functor s (->) f, Functor s (->) g) => Functor s (->) (Product f g) where
-    map f (Pair x y) = Pair (f <$> x) (f <$> y)
-
-instance Functor (NT (->)) (NT (->)) (Product f) where
-    map (NT f) = NT (\ (Pair x y) -> Pair x (f y))
-
-instance Functor (NT (->)) (NT (NT (->))) Product where
-    map (NT f) = NT (NT (\ (Pair x y) -> Pair (f x) y))
-
-instance Category s => Functor s (->) (Const a) where
-    map _ (Const a) = Const a
-
-instance Functor (->) (NT (->)) Const where
-    map f = NT (\ (Const a) -> Const (f a))
-
-instance Functor (->) (->) Identity where
-    map f (Identity a) = Identity (f a)
-
-instance Category s => Functor s (->) Proxy where
-    map _ Proxy = Proxy
-
-instance Functor (->) (->) ((,) a) where
-    map f (a, b) = (a, f b)
-
-instance Functor (->) (NT (->)) (,) where
-    map f = NT (\ (a, b) -> (f a, b))
-
-instance Functor (->) (->) (Either a) where
-    map _ (Left a) = Left a
-    map f (Right b) = Right (f b)
-
-instance Functor (->) (NT (->)) Either where
-    map f = NT (\ case Left a -> Left (f a)
-                       Right b -> Right b)
-
-instance Category s => Functor s (->) (s a) where
-    map = (.)
-
-instance Category s => Functor (Dual s) (NT (->)) s where
-    map (Dual f) = NT (. f)
diff --git a/Control/Category/Const2.hs b/Control/Category/Const2.hs
deleted file mode 100644
--- a/Control/Category/Const2.hs
+++ /dev/null
@@ -1,14 +0,0 @@
-module Control.Category.Const2 where
-
-import Algebra as A
-import Control.Category.Groupoid
-
-newtype Const2 a b c = Const2 a
-  deriving (Semigroup, Monoid, Group)
-
-instance Monoid a => Category (Const2 a) where
-    id = Const2 mempty
-    Const2 a . Const2 b = Const2 (a <> b)
-
-instance Group a => Groupoid (Const2 a) where
-    invert (Const2 a) = Const2 (A.invert a)
diff --git a/Control/Category/Dual.hs b/Control/Category/Dual.hs
deleted file mode 100644
--- a/Control/Category/Dual.hs
+++ /dev/null
@@ -1,13 +0,0 @@
-module Control.Category.Dual where
-
-import Control.Category.Groupoid
-
-newtype Dual k a b = Dual { dual :: k b a }
-  deriving (Semigroup, Monoid, Group)
-
-instance Category k => Category (Dual k) where
-    id = Dual id
-    Dual f . Dual g = Dual (g . f)
-
-instance Groupoid k => Groupoid (Dual k) where
-    invert = Dual . invert . dual
diff --git a/Control/Category/Groupoid.hs b/Control/Category/Groupoid.hs
deleted file mode 100644
--- a/Control/Category/Groupoid.hs
+++ /dev/null
@@ -1,4 +0,0 @@
-module Control.Category.Groupoid where
-
-class Category k => Groupoid k where
-    invert :: k a b -> k b a
diff --git a/Data/Morphism/Endo.hs b/Data/Morphism/Endo.hs
deleted file mode 100644
--- a/Data/Morphism/Endo.hs
+++ /dev/null
@@ -1,15 +0,0 @@
-module Data.Morphism.Endo where
-
-import Algebra as A
-import Control.Category.Groupoid as C
-
-newtype Endo s a = Endo { endo :: s a a }
-
-instance Category s => Semigroup (Endo s a) where
-    Endo f <> Endo g = Endo (f . g)
-
-instance Category s => Monoid (Endo s a) where
-    mempty = Endo id
-
-instance Groupoid s => Group (Endo s a) where
-    invert (Endo f) = Endo (C.invert f)
diff --git a/Data/Morphism/Iso.hs b/Data/Morphism/Iso.hs
deleted file mode 100644
--- a/Data/Morphism/Iso.hs
+++ /dev/null
@@ -1,30 +0,0 @@
-module Data.Morphism.Iso where
-
-import qualified Algebra as A
-import Control.Categorical.Functor
-import Control.Category.Dual
-import Control.Category.Groupoid
-
-data Iso s a b = Iso (s a b) (s b a)
-
-instance (Semigroup (s a b), Semigroup (s b a)) => Semigroup (Iso s a b) where
-    Iso f f' <> Iso g g' = Iso (f <> g) (f' <> g')
-
-instance (Monoid (s a b), Monoid (s b a)) => Monoid (Iso s a b) where
-    mempty = Iso mempty mempty
-
-instance (Group (s a b), Group (s b a)) => Group (Iso s a b) where
-    invert (Iso f f') = Iso (A.invert f) (A.invert f')
-
-instance Category s => Category (Iso s) where
-    id = Iso id id
-    Iso f f' . Iso g g' = Iso (f . g) (g' . f')
-
-instance Category s => Groupoid (Iso s) where
-    invert (Iso f f') = Iso f' f
-
-instance Functor s t f => Functor (Iso s) t f where
-    map (Iso f _) = map f
-
-instance Functor s t f => Functor (Iso s) (Dual t) f where
-    map (Iso _ f') = Dual (map f')
diff --git a/Prelude.hs b/Prelude.hs
deleted file mode 100644
--- a/Prelude.hs
+++ /dev/null
@@ -1,9 +0,0 @@
-module Prelude (module Control.Category,
-                module Data.Either,
-                Semigroup (..), Monoid (..), Group) where
-
-import Algebra (Group)
-import Control.Category
-import Data.Either
-import Data.Monoid (Monoid (..))
-import Data.Semigroup (Semigroup (..))
diff --git a/Setup.hs b/Setup.hs
--- a/Setup.hs
+++ b/Setup.hs
@@ -1,2 +1,3 @@
 import Distribution.Simple
+
 main = defaultMain
diff --git a/category.cabal b/category.cabal
--- a/category.cabal
+++ b/category.cabal
@@ -1,5 +1,5 @@
 name:                category
-version:             0.1.2.0
+version:             0.2.5.0
 synopsis:            Categorical types and classes
 -- description:         
 license:             BSD3
@@ -9,25 +9,52 @@
 -- copyright:           
 category:            Control, Math
 build-type:          Simple
-cabal-version:       >=1.10
+cabal-version:       >=1.22
+bug-reports:         http://github.com/strake/category.hs/issues
+tested-with:         GHC ==8.4.3
+                   , GHC ==8.6.4
 
 library
+  hs-source-dirs:      src
   exposed-modules:     Control.Categorical.Functor
+                     , Control.Categorical.Monad
                      , Control.Category.Const2
-                     , Control.Category.Dual
                      , Control.Category.Groupoid
+                     , Data.Functor.Trans.Identity
+                     , Data.Functor.Trans.Reader
+                     , Data.Functor.Trans.Writer
                      , Data.Morphism.Endo
                      , Data.Morphism.Iso
+  reexported-modules:  Control.Category.Dual
   other-modules:       Prelude
   build-depends:       base >=4.10 && <5
                      , alg >=0.2 && <0.3
+                     , dual >=0.1.0.2 && <0.2
+                     , transformers >= 0.5 && < 0.6
   default-language:    Haskell2010
   default-extensions:  UnicodeSyntax
                      , LambdaCase
+                     , PartialTypeSignatures
+                     , TypeOperators
                      , PolyKinds
                      , ConstraintKinds
                      , MultiParamTypeClasses
                      , FlexibleContexts
                      , FlexibleInstances
-                     , GeneralizedNewtypeDeriving
-  ghc-options:         -Wall
+                     , StandaloneDeriving
+                     , DerivingStrategies
+                     , DerivingVia
+                     , Safe
+  ghc-options:         -Wall -Wcompat -Wredundant-constraints -Wno-name-shadowing
+                       -Wincomplete-record-updates -Wincomplete-uni-patterns
+                       -Werror=incomplete-patterns
+                       -Werror=incomplete-uni-patterns
+                       -Werror=incomplete-record-updates
+                       -Werror=missing-fields
+                       -Werror=missing-methods
+                       -Wno-partial-type-signatures
+                       -Wno-simplifiable-class-constraints
+
+source-repository head
+  type: git
+  location: http://github.com/strake/category.hs.git
diff --git a/src/Control/Categorical/Functor.hs b/src/Control/Categorical/Functor.hs
new file mode 100644
--- /dev/null
+++ b/src/Control/Categorical/Functor.hs
@@ -0,0 +1,119 @@
+{-# LANGUAGE RankNTypes #-}
+
+module Control.Categorical.Functor where
+
+import Control.Category.Dual
+import Control.Category.Groupoid
+import Control.Monad.Trans.Identity (IdentityT (..))
+import qualified Data.Functor as Base
+import Data.Functor.Compose
+import Data.Functor.Identity
+import Data.Functor.Const
+import Data.Functor.Product
+import Data.Functor.Sum
+import Data.Proxy
+
+-- | Laws:
+--
+-- @
+-- 'map' 'id' = 'id'
+-- 'map' (f '.' g) = 'map' f '.' 'map' g
+-- @
+class (Category s, Category t) => Functor (s :: α -> α -> *) (t :: β -> β -> *) (f :: α -> β) where
+    map :: s a b -> t (f a) (f b)
+
+{-# DEPRECATED EndoFunctor "Use Endofunctor" #-}
+type EndoFunctor s = Functor s s
+type Endofunctor s = Functor s s
+
+infixl 4 <$>
+(<$>) :: Functor s (->) f => s a b -> f a -> f b
+(<$>) = map
+
+newtype NT s f g = NT { nt :: ∀ a . s (f a) (g a) }
+
+instance Category s => Category (NT s) where
+    id = NT id
+    NT f . NT g = NT (f . g)
+
+instance Groupoid s => Groupoid (NT s) where
+    invert (NT f) = NT (invert f)
+
+instance {-# INCOHERENT #-} Base.Functor f => Functor (->) (->) f where map = Base.fmap
+
+instance Functor s (->) f => Functor (NT s) (NT (->)) (Compose f) where
+    map (NT f) = NT (\ (Compose x) -> Compose (f <$> x))
+
+instance Functor (NT (->)) (NT (NT (->))) Compose where
+    map (NT f) = NT (NT (\ (Compose x) -> Compose (f x)))
+
+instance (Functor s (->) f, Functor s (->) g) => Functor s (->) (Sum f g) where
+    map f (InL x) = InL (f <$> x)
+    map f (InR y) = InR (f <$> y)
+
+instance Functor (NT (->)) (NT (->)) (Sum f) where
+    map (NT f) = NT (\ case InL x -> InL x
+                            InR y -> InR (f y))
+
+instance Functor (NT (->)) (NT (NT (->))) Sum where
+    map (NT f) = NT (NT (\ case InL x -> InL (f x)
+                                InR y -> InR y))
+
+instance (Functor s (->) f, Functor s (->) g) => Functor s (->) (Product f g) where
+    map f (Pair x y) = Pair (f <$> x) (f <$> y)
+
+instance Functor (NT (->)) (NT (->)) (Product f) where
+    map (NT f) = NT (\ (Pair x y) -> Pair x (f y))
+
+instance Functor (NT (->)) (NT (NT (->))) Product where
+    map (NT f) = NT (NT (\ (Pair x y) -> Pair (f x) y))
+
+instance Category s => Functor s (->) (Const a) where
+    map _ (Const a) = Const a
+
+instance Functor (->) (NT (->)) Const where
+    map f = NT (\ (Const a) -> Const (f a))
+
+instance Functor (->) (->) Identity where
+    map f (Identity a) = Identity (f a)
+
+instance Category s => Functor s (->) Proxy where
+    map _ Proxy = Proxy
+
+instance Functor (->) (->) ((,) a) where
+    map f (a, b) = (a, f b)
+
+instance Functor (->) (NT (->)) (,) where
+    map f = NT (\ (a, b) -> (f a, b))
+
+instance Functor (->) (->) (Either a) where
+    map _ (Left a) = Left a
+    map f (Right b) = Right (f b)
+
+instance Functor (->) (NT (->)) Either where
+    map f = NT (\ case Left a -> Left (f a)
+                       Right b -> Right b)
+
+instance Category s => Functor s (->) (s a) where
+    map = (.)
+
+instance Category s => Functor (Dual s) (NT (->)) s where
+    map (Dual f) = NT (. f)
+
+instance Functor s t f => Functor (Dual s) (Dual t) f where
+    map (Dual f) = Dual (map f)
+
+instance (Category t, Functor s (NT t) f) => Functor (Dual s) (NT (Dual t)) f where
+    map (Dual f) = NT (Dual (nt (map f)))
+
+instance (Category s, Category t, Functor s (NT (Dual t)) f) => Functor s (Dual (NT t)) f where
+    map f = Dual (NT (dual (nt (map f))))
+
+instance Functor (NT (->)) (NT (->)) IdentityT where
+    map f = NT (\ (IdentityT x) -> IdentityT (nt f x))
+
+instance Functor s (->) f => Functor s (->) (IdentityT f) where
+    map f = IdentityT . map f . runIdentityT
+
+instance (Category s, Category t, Functor (NT s) (NT t) f) => Functor (NT (Dual s)) (NT (Dual t)) f where
+    map f = NT (Dual (nt (map (NT (dual (nt f))))))
diff --git a/src/Control/Categorical/Monad.hs b/src/Control/Categorical/Monad.hs
new file mode 100644
--- /dev/null
+++ b/src/Control/Categorical/Monad.hs
@@ -0,0 +1,176 @@
+{-# LANGUAGE ScopedTypeVariables #-}
+{-# LANGUAGE ExistentialQuantification #-}
+module Control.Categorical.Monad (Monad (..), (<=<), (>=>), Kleisli (..), Comonad (..), (=<=), (=>=), Cokleisli (..)) where
+
+import qualified Control.Applicative as Base
+import qualified Control.Monad as Base
+import Control.Monad.Trans.Identity (IdentityT (..))
+import Data.Function (($), flip)
+import Data.Functor.Identity
+import Data.List.NonEmpty (NonEmpty (..))
+import qualified Data.List.NonEmpty as NE
+import Data.Semigroup (Arg (..))
+import qualified Data.Traversable as Base
+
+import Control.Categorical.Functor
+import Control.Category.Dual
+
+infixr 1 >=>, <=<, =>=, =<=
+
+class Endofunctor s m => Monad s m where
+    unit :: a `s` m a
+
+    join :: m (m a) `s` m a
+    join = bind id
+
+    bind :: a `s` m b -> m a `s` m b
+    bind f = join . map f
+
+(<=<) :: Monad s m => b `s` m c -> a `s` m b -> a `s` m c
+f <=< g = bind f . bind g . unit
+
+(>=>) :: Monad s m => a `s` m b -> b `s` m c -> a `s` m c
+(>=>) = flip (<=<)
+
+newtype Kleisli s m a b = Kleisli { kleisli :: a `s` m b }
+
+instance Monad s m => Category (Kleisli s m) where
+    id = Kleisli unit
+    Kleisli f . Kleisli g = Kleisli (f <=< g)
+
+instance {-# INCOHERENT #-} Base.Monad m => Monad (->) m where
+    unit = Base.return
+    join = Base.join
+    bind = (Base.=<<)
+
+instance Comonad s f => Monad (Dual s) f where
+    unit = Dual counit
+    join = Dual cut
+
+instance (Category s, Comonad (NT s) f) => Monad (NT (Dual s)) f where
+    unit = NT (Dual (nt counit))
+    join = NT (Dual (nt cut))
+
+class Endofunctor s ɯ => Comonad s ɯ where
+    counit :: ɯ a `s` a
+
+    cut :: ɯ a `s` ɯ (ɯ a)
+    cut = cobind id
+
+    cobind :: ɯ a `s` b -> ɯ a `s` ɯ b
+    cobind f = map f . cut
+
+(=<=) :: Comonad s ɯ => ɯ b `s` c -> ɯ a `s` b -> ɯ a `s` c
+f =<= g = counit . cobind f . cobind g
+
+(=>=) :: Comonad s ɯ => ɯ a `s` b -> ɯ b `s` c -> ɯ a `s` c
+(=>=) = flip (=<=)
+
+newtype Cokleisli s ɯ a b = Cokleisli { cokleisli :: ɯ a `s` b }
+
+instance Comonad s ɯ => Category (Cokleisli s ɯ) where
+    id = Cokleisli counit
+    Cokleisli f . Cokleisli g = Cokleisli (f =<= g)
+
+instance Comonad (->) Identity where
+    counit = runIdentity
+    cut = map Identity
+
+instance Comonad (->) NonEmpty where
+    counit = NE.head
+    cut (x:|xs) = (x:|xs) :| go xs
+      where go [] = []
+            go (x:xs) = (x:|xs) : go xs
+
+instance Monoid m => Comonad (->) ((->) m) where
+    counit = ($ mempty)
+    cut f x y = f (x <> y)
+
+instance Comonad (->) ((,) a) where
+    counit (_, b) = b
+    cut (a, b) = (a, (a, b))
+
+instance Comonad (->) (Arg a) where
+    counit (Arg _ b) = b
+    cut (Arg a b) = Arg a (Arg a b)
+
+instance Functor s t m => Functor s (->) (Kleisli t m a) where
+    map f (Kleisli φ) = Kleisli (map f . φ)
+
+instance Category s => Functor s (->) (Cokleisli s ɯ a) where
+    map f (Cokleisli φ) = Cokleisli (f . φ)
+
+instance Category s => Functor (Dual s) (NT (->)) (Kleisli s m) where
+    map (Dual f) = NT (\ (Kleisli φ) -> Kleisli (φ . f))
+
+instance Functor s t ɯ => Functor (Dual s) (NT (->)) (Cokleisli t ɯ) where
+    map (Dual f) = NT (\ (Cokleisli φ) -> Cokleisli (φ . map f))
+
+instance Monad s m => Functor (Kleisli s m) s m where
+    map = bind . kleisli
+
+instance Comonad s ɯ => Functor (Cokleisli s ɯ) s ɯ where
+    map = cobind . cokleisli
+
+instance {-# OVERLAPPABLE #-} (Base.Traversable f, Monad (->) m) => Functor (Kleisli (->) m) (Kleisli (->) m) f where
+    map (Kleisli f) = Kleisli (unBaseMonad . Base.traverse (BaseMonad . f))
+
+data BaseMonad m a = Monad (->) m => BaseMonad { unBaseMonad :: m a }
+instance Base.Functor (BaseMonad f) where fmap = map
+instance Base.Applicative (BaseMonad m) where pure = unit; (<*>) = Base.ap
+instance Base.Monad (BaseMonad m) where (>>=) = flip bind
+
+instance Monad (->) m => Functor (NT (Kleisli (->) m)) (NT (Kleisli (->) m)) IdentityT where
+    map f = NT (Kleisli (map IdentityT . kleisli (nt f) . runIdentityT))
+
+instance Monad (Dual (->)) m => Functor (NT (Kleisli (Dual (->)) m)) (NT (Kleisli (Dual (->)) m)) IdentityT where
+    map f = NT (Kleisli (Dual (IdentityT . dual (kleisli (nt f)) . dual (map (Dual runIdentityT)))))
+
+instance Comonad (->) ɯ => Functor (NT (Cokleisli (->) ɯ)) (NT (Cokleisli (->) ɯ)) IdentityT where
+    map f = NT (Cokleisli (IdentityT . cokleisli (nt f) . map runIdentityT))
+
+instance Monad (NT (->)) IdentityT where
+    unit = NT IdentityT
+    join = NT runIdentityT
+
+instance Comonad (NT (->)) IdentityT where
+    counit = NT runIdentityT
+    cut = NT IdentityT
+
+instance Monad (->) m => Monad (NT (Kleisli (->) m)) IdentityT where
+    unit = NT (Kleisli (unit . IdentityT))
+    join = NT (Kleisli (unit . runIdentityT))
+
+instance Comonad (->) ɯ => Monad (NT (Cokleisli (->) ɯ)) IdentityT where
+    unit = NT (Cokleisli (IdentityT . counit))
+    join = NT (Cokleisli (runIdentityT . counit))
+
+instance Comonad (->) ɯ => Comonad (NT (Cokleisli (->) ɯ)) IdentityT where
+    counit = NT (Cokleisli (runIdentityT . counit))
+    cut = NT (Cokleisli (IdentityT . counit))
+
+instance Monad (->) m => Comonad (NT (Kleisli (->) m)) IdentityT where
+    counit = NT (Kleisli (unit . runIdentityT))
+    cut = NT (Kleisli (unit . IdentityT))
+
+instance Monad (->) f => Monad (->) (IdentityT f) where
+    unit = IdentityT . unit
+    join = IdentityT . bind runIdentityT . runIdentityT
+
+instance Comonad (->) f => Comonad (->) (IdentityT f) where
+    counit = counit . runIdentityT
+    cut = runIdentityT . cobind runIdentityT . IdentityT
+
+instance (Functor s (Kleisli (->) m) f, Endofunctor (->) m) =>
+         Functor s (Kleisli (->) m) (IdentityT f) where
+    map f = Kleisli (map IdentityT . kleisli (map f) . runIdentityT)
+
+instance (Functor s (Cokleisli (->) ɯ) f, Endofunctor (->) ɯ) =>
+         Functor s (Cokleisli (->) ɯ) (IdentityT f) where
+    map f = Cokleisli (IdentityT . cokleisli (map f) . map runIdentityT)
+
+instance (Monad (->) m) => Functor (Kleisli (->) m) (Kleisli (->) m) ((,) a) where
+    map (Kleisli f) = Kleisli (\ (a, b) -> (,) a <$> f b)
+
+instance (Monad (->) m) => Functor (Kleisli (->) m) (NT (Kleisli (->) m)) (,) where
+    map (Kleisli f) = NT (Kleisli (\ (a, b) -> (\ a -> (a, b)) <$> f a))
diff --git a/src/Control/Category/Const2.hs b/src/Control/Category/Const2.hs
new file mode 100644
--- /dev/null
+++ b/src/Control/Category/Const2.hs
@@ -0,0 +1,24 @@
+module Control.Category.Const2 where
+
+import Algebra as A
+import Control.Categorical.Functor
+import Control.Categorical.Monad
+import Control.Category.Groupoid
+import Relation.Binary.Comparison
+
+-- | Notes: 'Const2' '()' is the indiscrete category.
+newtype Const2 a b c = Const2 { getConst2 :: a }
+  deriving (Semigroup, Monoid, Group, PartialEq, Preord, Eq, PartialOrd, Ord) via a
+
+instance Functor (->) (NT (NT (->))) Const2 where
+    map f = NT (NT (\ (Const2 a) -> Const2 (f a)))
+
+instance Monad (->) m => Functor (Kleisli (->) m) (NT (NT (Kleisli (->) m))) Const2 where
+    map (Kleisli f) = NT (NT (Kleisli (\ (Const2 a) -> Const2 <$> f a)))
+
+instance (Semigroup a, Monoid a) => Category (Const2 a) where
+    id = Const2 mempty
+    Const2 a . Const2 b = Const2 (a <> b)
+
+instance (Semigroup a, Group a) => Groupoid (Const2 a) where
+    invert (Const2 a) = Const2 (A.invert a)
diff --git a/src/Control/Category/Groupoid.hs b/src/Control/Category/Groupoid.hs
new file mode 100644
--- /dev/null
+++ b/src/Control/Category/Groupoid.hs
@@ -0,0 +1,16 @@
+module Control.Category.Groupoid where
+
+import Control.Category.Dual
+
+-- | 'Category' where every morphism is iso
+--
+-- Laws:
+--
+-- @
+-- 'id' = f '.' 'invert' f
+-- 'id' = 'invert' f '.' f
+-- @
+class Category k => Groupoid k where
+    invert :: k a b -> k b a
+
+instance Groupoid k => Groupoid (Dual k) where invert = Dual . invert . dual
diff --git a/src/Data/Functor/Trans/Identity.hs b/src/Data/Functor/Trans/Identity.hs
new file mode 100644
--- /dev/null
+++ b/src/Data/Functor/Trans/Identity.hs
@@ -0,0 +1,3 @@
+module Data.Functor.Trans.Identity (IdentityT (..)) where
+
+import Control.Monad.Trans.Identity (IdentityT (..))
diff --git a/src/Data/Functor/Trans/Reader.hs b/src/Data/Functor/Trans/Reader.hs
new file mode 100644
--- /dev/null
+++ b/src/Data/Functor/Trans/Reader.hs
@@ -0,0 +1,37 @@
+{-# LANGUAGE RankNTypes #-}
+
+module Data.Functor.Trans.Reader where
+
+import Control.Categorical.Functor
+import Control.Categorical.Monad
+import Data.Function (flip)
+
+newtype ReaderT s r f a = ReaderT { runReaderT :: r `s` f a }
+
+instance {-# INCOHERENT #-} Functor s t f => Functor s (->) (ReaderT t r f) where
+    map f (ReaderT x) = ReaderT (map f . x)
+
+instance (Functor t (->) f, Functor (->) (->) (s r)) => Functor t (->) (ReaderT s r f) where
+    map f (ReaderT x) = ReaderT ((map f :: _ -> _) <$> x)
+
+instance Monad (->) f => Monad (->) (ReaderT (->) r f) where
+    unit = ReaderT . unit . unit
+    join (ReaderT x) = ReaderT (\ r -> (flip id r >=> flip runReaderT r) x)
+
+instance Comonad (->) ɯ => Comonad (->) (ReaderT (,) r ɯ) where
+    counit = counit . counit . runReaderT
+    cut (ReaderT (r, x)) = ReaderT (r, cobind (ReaderT . (,) r) x)
+
+instance (Functor t (->) (s r)) => Functor (NT t) (NT (->)) (ReaderT s r) where
+    map f = NT (\ (ReaderT x) -> ReaderT (nt f <$> x))
+
+instance Monad (->) (s r) => Monad (NT (->)) (ReaderT s r) where
+    unit = NT (ReaderT . unit)
+    join = NT (ReaderT . bind runReaderT . runReaderT)
+
+instance Comonad (->) (s r) => Comonad (NT (->)) (ReaderT s r) where
+    counit = NT (counit . runReaderT)
+    cut = NT (ReaderT . cobind ReaderT . runReaderT)
+
+instance Functor t (NT (->)) s => Functor t (NT (NT (->))) (ReaderT s) where
+    map f = NT (NT (\ (ReaderT x) -> ReaderT (nt (map f) x)))
diff --git a/src/Data/Functor/Trans/Writer.hs b/src/Data/Functor/Trans/Writer.hs
new file mode 100644
--- /dev/null
+++ b/src/Data/Functor/Trans/Writer.hs
@@ -0,0 +1,25 @@
+module Data.Functor.Trans.Writer where
+
+import Control.Categorical.Functor
+import Control.Categorical.Monad
+
+newtype WriterT p w f a = WriterT { runWriterT :: f (p w a) }
+
+instance (Functor (->) (->) f, Functor s (->) (p w)) => Functor s (->) (WriterT p w f) where
+    map f (WriterT x) = WriterT ((map f :: _ -> _) <$> x)
+
+instance (Monoid w, Monad (->) f) => Monad (->) (WriterT (,) w f) where
+    unit = WriterT . unit . unit
+    join = WriterT . bind (\ (w, WriterT y) -> map (\ (w', a) -> (w <> w', a)) y) . runWriterT
+
+instance (Comonad (->) (p w), Comonad (->) f) => Comonad (->) (WriterT p w f) where
+    counit = counit . counit . runWriterT
+    cut = WriterT . cobind (\ x -> (\ _ -> WriterT x) <$> counit x) . runWriterT
+
+instance Monad (->) f => Monad (->) (WriterT Either w f) where
+    unit = WriterT . unit . unit
+    join = WriterT . bind (\ case Left w -> unit (Left w)
+                                  Right (WriterT x) -> x) . runWriterT
+
+instance Functor (NT (->)) (NT (->)) (WriterT p w) where
+    map f = NT (\ (WriterT x) -> WriterT (nt f x))
diff --git a/src/Data/Morphism/Endo.hs b/src/Data/Morphism/Endo.hs
new file mode 100644
--- /dev/null
+++ b/src/Data/Morphism/Endo.hs
@@ -0,0 +1,16 @@
+module Data.Morphism.Endo where
+
+import Algebra as A
+import Control.Category.Groupoid as C
+
+newtype Endo s a = Endo { endo :: s a a }
+
+instance Category s => Semigroup (Endo s a) where
+    Endo f <> Endo g = Endo (f . g)
+
+instance Category s => Monoid (Endo s a) where
+    mappend = (<>)
+    mempty = Endo id
+
+instance Groupoid s => Group (Endo s a) where
+    invert (Endo f) = Endo (C.invert f)
diff --git a/src/Data/Morphism/Iso.hs b/src/Data/Morphism/Iso.hs
new file mode 100644
--- /dev/null
+++ b/src/Data/Morphism/Iso.hs
@@ -0,0 +1,33 @@
+module Data.Morphism.Iso where
+
+import qualified Algebra as A
+import Control.Categorical.Functor
+import Control.Category.Dual
+import Control.Category.Groupoid
+
+data Iso s a b = Iso (s a b) (s b a)
+
+instance (Semigroup (s a b), Semigroup (s b a)) => Semigroup (Iso s a b) where
+    Iso f f' <> Iso g g' = Iso (f <> g) (f' <> g')
+
+instance (Semigroup (s a b), Semigroup (s b a),
+          Monoid (s a b), Monoid (s b a)) => Monoid (Iso s a b) where
+    mappend = (<>)
+    mempty = Iso mempty mempty
+
+instance (Semigroup (s a b), Semigroup (s b a),
+          Group (s a b), Group (s b a)) => Group (Iso s a b) where
+    invert (Iso f f') = Iso (A.invert f) (A.invert f')
+
+instance Category s => Category (Iso s) where
+    id = Iso id id
+    Iso f f' . Iso g g' = Iso (f . g) (g' . f')
+
+instance Category s => Groupoid (Iso s) where
+    invert (Iso f f') = Iso f' f
+
+instance Functor s t f => Functor (Iso s) t f where
+    map (Iso f _) = map f
+
+instance Functor s t f => Functor (Iso s) (Dual t) f where
+    map (Iso _ f') = Dual (map f')
diff --git a/src/Prelude.hs b/src/Prelude.hs
new file mode 100644
--- /dev/null
+++ b/src/Prelude.hs
@@ -0,0 +1,9 @@
+module Prelude (module Control.Category,
+                module Data.Either,
+                Semigroup (..), Monoid (..), Group) where
+
+import Algebra (Group)
+import Control.Category
+import Data.Either
+import Data.Monoid (Monoid (..))
+import Data.Semigroup (Semigroup (..))