category-theory-presentation/categories/30_How/200_Monads/050_Composition_problem.md

Composition problem

The Problem; example with lists:

f x = [x]       ⇒ f 1 = [1]   ⇒ (f.f) 1 = [[1]] ✗
g x = [x+1]     ⇒ g 1 = [2]   ⇒ (g.g) 1 = ERROR [2]+1 ✗
h x = [x+1,x*3] ⇒ h 1 = [2,3] ⇒ (h.h) 1 = ERROR [2,3]+1 ✗ 

The same problem with most f :: a -> F a functions and functor F.