Daryoush Mehrtash <dmehrt...@gmail.com> wrote: > In category theory functors are defined between two category of C and > D where every object and morphism from C is mapped to D. > > I am trying to make sense of the above definition with functor class > in Haskell. Let say I am dealing with List type. When I define List > to be a instance of a functor I am saying the source category (C) is > Haskell types and the destination category is List (D). In this the > "fmap" is implementation of the mapping between every morphism in my > Haskell Categroy (C) to morphism in List cataegory (D). With type > constructor I also have the mapping of types (objects in Haskell > Category, or my source cataegroy C) to List category (D). So my > functor in the catarogy sense is actually the fmap and type > constructor. Am I remotely correct?
The type constructors map objects from C to objects from F(C). The 'fmap' function maps morphisms from C to morphisms from F(C). You can see this immediately by looking at the type of 'fmap' (note that (->) is right-associative): fmap :: Functor f => (a -> b) -> (f a -> f b) Greets, Ertugrul. -- nightmare = unsafePerformIO (getWrongWife >>= sex) http://blog.ertes.de/ _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
