úÎ#BéQ      !"#$%&'()*+,-./012345678 9 : ; < = > ? @ A B C D E F G H I J K L M N O P  ,A representation of a contravariant functor #An adjunction from Hask^op to Hask   Op (f a) b ~ Hask a (g b)  rightAdjunct unit = id  leftAdjunct counit = id  :Represent a contravariant functor that has a left adjoint Q'This gives rise to the Cont Bool monad R-This adjunction gives rise to the Cont monad    MPTCs, fundeps provisionalEdward Kmett <ekmett@gmail.com>     MPTCs, fundeps provisionalEdward Kmett <ekmett@gmail.com>#An adjunction from Hask to Hask^op   Hask (f a) b ~ Op a (g b)  rightAdjunct unit = id  leftAdjunct counit = id rank 2 types, MPTCs, fundeps experimentalEdward Kmett <ekmett@gmail.com>  !%An adjunction between Hask and Hask.  rightAdjunct unit = id  leftAdjunct counit = id "#$%&  !"#$%& !"#$% &   !"#$%"#$%&MPTCs, fundeps provisionalEdward Kmett <ekmett@gmail.com>'()*+,'()*+,*,+'()'()()*+,non-portable (GADTs, MPTCs) experimentalEdward Kmett <ekmett@gmail.com>-./WThe natural isomorphism between a comonad w and the comonad generated by w (forwards). 01-./01-./01-../01MPTCs, fundeps provisionalEdward Kmett <ekmett@gmail.com>234567SiExploiting this instance requires that we have the missing Traversables for Identity, (,)e and IdentityT 23456757623423434567 "non-portable (rank-2 polymorphism) provisionalEdward Kmett <ekmett@gmail.com>89:;<=89:;<=89:;<=89:9:;<= rank-2 types, MPTCs experimentalEdward Kmett <ekmett@gmail.com>>?@ABCDETFGHIJ >?@ABCDEFGHIJ ABCDEFG>?@HIJ >?@?@ABCBCDEFGHIJ MPTCs provisionalEdward Kmett <ekmett@gmail.com>KLMNOPKLMNOPNPOKLMKLMLMNOPU    !"#$%   &&'() * * + , - . / / 0 1 1 2 3 4 5 6 7 8 9      :;< =>adjunctions-0.4.0%Data.Functor.Contravariant.AdjunctionControl.Monad.Contra.AdjointControl.Monad.Contra.Cont)Data.Functor.Contravariant.DualAdjunctionData.Functor.AdjunctionControl.Comonad.Trans.AdjointControl.Comonad.Trans.DensityControl.Monad.Trans.AdjointControl.Monad.Trans.CodensityData.Functor.ZapControl.Comonad.Contra.AdjointRepresentationrepunrep Adjunctionunitcounit leftAdjunct rightAdjunct repAdjunctionrepFlippedAdjunctionAdjointT runAdjointTAdjointadjoint runAdjointContTrunContTContcontrunContcallCCDualAdjunctionunitOpcounitOp leftAdjunctOprightAdjunctOpDensity liftDensitydensityToAdjunctionadjunctionToDensity Codensity runCodensitylowerCodensitycodensityToAdjunctionadjunctionToCodensityBizap bizapWithZapzapWithzapflipZap zapAdjunction composeZapbizap flipBizapbizapProductSum$fAdjunctionPredicatePredicate$fAdjunctionOpOp$fMonadTransAdjointTstrength