Theorem: Let $\mathcal{C}$ and $\mathcal{D}$ be a small category and let $F,G:\mathcal{C}\to\mathcal{D}$ be two functors. Then we have $\mathrm{Nat}(F,G)\cong \int_{c\in\mathcal{C}}\hom_{\mathcal{D}}(F(c),G(c))$.
Theorem: Let $\mathcal{C}$ and $\mathcal{D}$ be a small category and let $F,G:\mathcal{C}\to\mathcal{D}$ be two functors. Then we have $\mathrm{Nat}(F,G)\cong \int_{c\in\mathcal{C}}\hom_{\mathcal{D}}(F(c),G(c))$.