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


Generalizations