presheaf

presheaf englanniksi

1. An abstract mathematical construct which associates data to the sets of a space, generalizing the situation of functions, bundles, manifold structure, etc. on a topological space (but not necessarily in such a way as to make the local and global data compatible, as in a sheaf). Formally, A functor \mathcal{F} whose domain is a category whose objects are sets of a space (called the space or space) and whose morphisms are mappings. The image of each open set under \mathcal{F} is an object whose elements are called sections, and are which are said to be ''over'' the given open set; the image of each inclusion map A \to B under \mathcal{F} is a morphism \mathcal{F}(B) \to \mathcal{F}(A), called the restriction from B to A and denoted \operatorname{res}_{B,A} or |_{B,A}.jocaps. "presheaf of a topological basis". PlanetMath.org. Freely available at http://planetmath.org/presheafofatopologicalbasis