\begin{definition}[Definition:Presheaf on Topological Space/Definition 2]
Let $T = \left({S, \tau}\right)$ be a topological space.
Let $\mathbf C$ be a category.
Let $\tau$ be the category of open sets of $T$.
A $\mathbf C$-valued '''presheaf''' on $T$ is a contravariant functor $\tau \to \mathbf C$.
\end{definition}