I am reading [this paper][1] on Homotopy for functors by Ming-Jung 
 Lee.

The author gives a definition (at the beginning of section $3$) as follows : 

> Let $\varphi,\varphi':\Lambda\rightarrow \Gamma$ be covariant functors of small categories. We say that $\varphi$ is homotopic to $\varphi'$ if there are covariant functors $\varphi_i:\Lambda\rightarrow \Gamma$ for $i=0,1,\cdots,n$ such that $\varphi_0=\varphi,\varphi_n=\varphi'$ and for each $i$, there is a natural transformation between $\varphi_i$ and $\varphi_{i+1}$.



 Given two natural transformations, there is an obvious way to compose them which gives a natural transformation.

> What is the point of considering the finite collection of natural transformations between given two functors. We can just define that two functors are homotopic if there is a natural transformation between them. 

I do not understand what I am missing. Any suggestions are helpful.
 


  [1]: http://www.ams.org/journals/proc/1972-036-02/S0002-9939-1972-0334212-5/S0002-9939-1972-0334212-5.pdf