Definition:Sheaf on Topological Space

Definition
Let $T = \left({S, \tau}\right)$ be a topological space.

Let $\mathbf C$ be a category.

Empty set
The condition that $\mathcal F(\varnothing)$ is a final object of $\mathbf C$ is often added. But this is automatic, see Limit of Empty Diagram is Final Object.

Also see

 * Equivalence of Definitions of Sheaf on Topological Space


 * Definition:Category of Sheaves on Topological Space