Definition:Sheaf on Topological Space/Definition 4
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Definition
Let $T = \struct {S, \tau}$ be a topological space.
Let $\mathbf C$ be a category.
A $\mathbf C$-valued sheaf $\FF$ on $T$ is a $\mathbf C$-valued presheaf such that for all objects $X$ of $\mathbf C$ the presheaf of sets $\FF_X$ defined by
- $\FF_X(U) := \mathrm{Hom}_{\mathbf C}(X, \FF(U))$
is a sheaf of sets on $T$.