Definition:Presheaf on Topological Space/Definition 2

Definition
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 $\tau \to \mathbf C$.

Also see

 * Equivalence of Definitions of Presheaf on Topological Space