Definition:Morphism of Sheaves

Definition
Let $X$ be a topological space.

Let $\mathbf C$ be a category.

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

A sheaf morphism from $\mathcal F$ to $\mathcal G$ is a presheaf morphism $\mathcal F \to\mathcal G$.

Also see

 * Definition:Category of Sheaves on Topological Space