\begin{definition}[Definition:Category of Presheaves on Topological Space]
Let $X$ be a topological space. 
Let $\mathbf C$ be a category.
The '''category of $\mathbf C$-valued presheaves on $X$''' is the category with:
{{DefineCategory
|ob = $\mathbf C$-valued presheaves on $X$
|mor = morphisms of presheaves
|id = identity morphisms on presheaves
|comp = composition of morphisms of presheaves
}}
\end{definition}