I am not sure I follow how the endofunctor gave me the 2nd functor. As I read the transformation there are two catagories C and D and two functors F and G between the same two catagories. My problem is that I only have one functor between the Hask and List catagories. So where does the 2nd functor come into picture that also maps between the same C and D catagories?
Thanks Daryoush On Tue, Apr 21, 2009 at 4:01 PM, Dan Weston <weston...@imageworks.com>wrote: > You are on the right track. The usual construction is that Hask is the > category (with types as objects and functions as morphisms). > > Functor F is then an endofunctor taking Hask to itself: > > a -> F a > f -> fmap f > > So, for F = []: > > a -> [a] > f -> map f > > Natural transformations are then any fully polymorphic (no context) unary > function. The polymorphism is what makes them natural, since there is no > method to treat one object (type) different from another. > > > Daryoush Mehrtash 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? >> >> If this is correct.... With this example, then can you then help me >> understand the transformation between functors and natural transformations? >> Specifically, what does it means to have two different functors between >> Haskell cateogry and List category? >> Thanks, >> >> Daryoush >> >> >> >> >
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