Definition:Sheaf on Topological Space

Definition
Let $T = \struct {S, \tau}$ be a topological space.

Let $\mathbf C$ be a category.

Also defined as
The condition that $\map \FF \O$ is a final object of $\mathbf C$ is often added.

However, this property follows from the definition.

Also see

 * Definition:Sheaf of Sets on Topological Space


 * Sheaf of Sets iff Set-Valued Sheaf


 * Equivalence of Definitions of Sheaf on Topological Space


 * Definition:Category of Sheaves on Topological Space


 * Limit of Empty Diagram is Final Object, demonstrating that $\map \FF \O$ is a final object of $\mathbf C$