squares-0.2: The double category of Hask functors and profunctors
LicenseBSD-style (see the file LICENSE)
Maintainersjoerd@w3future.com
Safe HaskellSafe-Inferred
LanguageHaskell2010

Data.Functor.Adjunction.Square

Description

 
Synopsis

Documentation

leftAdjunct :: Adjunction f g => Square '[Costar f] '[Star g] '[] '[] Source #

+-----+
|     |
f<-@->g
|     |
+-----+
leftAdjunct = unit === (toLeft ||| toRight)

rightAdjunct :: Adjunction f g => Square '[Star g] '[Costar f] '[] '[] Source #

+-----+
|     |
g>-@-<f
|     |
+-----+
rightAdjunct = (fromLeft ||| fromRight) === counit

unit :: Adjunction f g => Square '[] '[] '[] '[f, g] Source #

+-----+
|     |
| /@\ |
| v v |
+-f-g-+
unit = fromRight ||| leftAdj ||| fromLeft

counit :: Adjunction f g => Square '[] '[] '[g, f] '[] Source #

+-g-f-+
| v v |
| \@/ |
|     |
+-----+
counit = toRight ||| rightAdjoint ||| toLeft