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

Author gives a definition (in 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 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.

I am reading this paper 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.