Definition:Morphism of Presheaves on Topological Space

Definition
Let $X$ be a topological space.

Let $\mathbf C$ be a category.

Let $\mathcal F$ and $\mathcal G$ be $\mathbf C$-valued presheaves on $X$.

Definition 2
A morphism of presheaves from $\mathcal F$ to $\mathcal G$ is a natural transformation $\mathcal F \to \mathcal G$.

Also see

 * Definition:Category of Presheaves on Topological Space