Presheaf (category theory)

In category theory, a branch of mathematics, a presheaf on a category ${\displaystyle C}$ is a functor ${\displaystyle F\colon C^{\mathrm {op} }\to \mathbf {Set} }$. If ${\displaystyle C}$ is the poset of open sets in a topological space, interpreted as a category, then one recovers the usual notion of presheaf on a topological space.

...
Wikipedia