 categoryextras0.53.6: Various modules and constructs inspired by category theory  Contents  Index 

Control.Functor.Full  Portability  nonportable (classassociated types)  Stability  experimental  Maintainer  Edward Kmett <ekmett@gmail.com> 



Description 


Synopsis 



Documentation 

class Functor f => Full f where 
A Full Functor F : C > D provides for every pair of objects c, c' in C
and every morphism g : F c > F c'l in D, a morphism g' : c > c' in C. In short
map has a rightinverse under composition.
fmap . premap = id
  Methods  premap :: (f a > f b) > a > b 
  Instances  


class Functor f => Faithful f 
 Instances  


unmap :: (Full f, Faithful f) => (f a > f b) > a > b 
For every pair of objects a and b in C a Full Faithful Functor F : C > D maps every morphism
f : a > b onto a distinct morphism f : T a > T b (since it is faithful) and every morphism from
g : T a > T b can be obtained from some f. (It maps Homsets bijectively, or in short fmap has both
a left and right inverse under composition.
unmap . fmap = id


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