presheaf

An abstract mathematical construct which associates data to the open sets of a topological space, generalizing the situation of functions, fiber 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 contravariant functor F whose domain is a category whose objects are open sets of a topological space (called the base space or underlying space) and whose morphisms are inclusion mappings. The image of each open set under 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→B under F is a morphism F(B)→F(A), called the restriction from B to A and denoted operatorname res_(B,A) or |_(B,A).

Definition source: English Wiktionary via Wiktextract

Qualifier: sheaf theory

Topics: category-theory, computing, engineering, mathematics, natural-sciences, physical-sciences, sciences

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