[Haskell-cafe] What do you call Applicative Functor Morphism?

[Ross Paterson]

On Fri, Nov 05, 2010 at 11:49:27PM -0400, roconnor at theorem.ca wrote:
> An applicative functor morphism is a polymorphic function,
> eta : forall a. A1 a -> A2 a between two applicative functors A1 and
> A2 that preserve pure and <*>:
> 
> eta (pure c) = pure c
> eta (f <*> x) = eta f <*> eta x
> 
> What do you guys call such a thing?  My leading candidate is
> "idomatic transformation".

An applicative functor is a functor with some extra structure.  Such a
function is a natural transformation between the underlying functors
that preserves the extra structure.  So "applicative transformation"
seems a logical name.