Presheaf (category theory)

In category theory, a branch of mathematics, a presheaf on a category C {\displaystyle C} is a functor F : C o p → S e t {\displaystyle F\colon C^{\mathrm {op} }\to \mathbf {Set} } . If C {\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.