Definition:Category of Sheaves on Topological Space

Definition
Let $X$ be a topological space.

Let $\mathbf C$ be a category.

The category of $\mathbf C$-valued sheaves on $X$ is the category with:

Also see

 * Definition:Category of Presheaves on Topological Space
 * Category of Abelian Sheaves on Topological Space is Abelian