Kerodon

Remark 1.5.3.10. Let $\operatorname{\mathcal{C}}$ and $\operatorname{\mathcal{D}}$ be $\infty $-categories, and suppose we are given a pair of functors $F,G: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$. We define a natural transformation from $F$ to $G$ to be a map of simplicial sets $u: \Delta ^1 \times \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ satisfying $u|_{ \{ 0\} \times \operatorname{\mathcal{C}}} = F$ and $u|_{ \{ 1\} \times \operatorname{\mathcal{C}}} = G$. In other words, a natural transformation from $F$ to $G$ is a morphism from $F$ to $G$ in the $\infty $-category $\operatorname{Fun}(\operatorname{\mathcal{C}}, \operatorname{\mathcal{D}})$.