sheaf
Meanings
noun
- A quantity of the stalks and ears of wheat, rye, or other grain, bound together; a bundle of grain or straw.
- Any collection of things bound together.
- A bundle of arrows sufficient to fill a quiver, or the allowance of each archer.
- A quantity of arrows, usually twenty-four.
- A sheave.
- 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 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:
- If two sections over U agree under restriction to every U_i, then the sections are the same.
- Given a family of sections s_i∈ℱ(U_i) such that all pairs (s_i,s_j) agree under restriction to U_i∩U_j, there is a (unique) section s over U whose restriction to U_i is s_i.
verb
- To gather and bind into a sheaf; to make into sheaves
- To collect and bind cut grain, or the like; to make sheaves.
Pronunciation
Word forms
Etymology
From Middle English scheef, from Old English sċēaf, from Proto-West Germanic *skaub, from Proto-Germanic *skauba- (“sheaf”). Cognates Akin to West Frisian skeaf (“sheaf”), Dutch schoof (“sheaf”), German Schaub, Old Norse skauf (“a fox's tail”). Compare further Gothic 𐍃𐌺𐌿𐍆𐍄 (skuft, “hair of the head”), German Schopf (“tuft”).
Synonyms
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