sheaf in Japanese

A quantity of the stalks and ears of wheat, rye, or other grain, bound together; a bundle of grain or straw.

(mathematics) An abstract construct in topology that associates data to the open sets of a topological space (i.e. a presheaf) in such a way so as to make the local and global data compatible, generalizing the situation of functions, fiber bundles, manifold structure, etc. on a topological space. Formally, a presheaf \mathcal{F} whose sections are, in a technical sense, uniquely determined by their restrictions onto smaller sets: that is, given an open cover \{U_i \} of U: