Definition:Restriction of Presheaf to Open Set
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Definition
Let $C$ be a category.
Let $X$ be a topological space.
Let $\FF$ be a $C$-valued presheaf on $X$.
Let $U \subset X$ be open.
The restriction of $\FF$ to $U$ is the restriction of the contravariant functor $\FF$ to the subcategory $U$.
Also see
- Definition:Restriction of Presheaf to Open Set Functor
- Restriction of Sheaf to Open Set is Sheaf
- Definition:Section of Presheaf Functor