What is the meaning of 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 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 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 under is a morphism , called the restriction from to and denoted or .
Source: wiktionary.org
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