sheaf

== English == === Etymology === From Middle English scheef, from Old English sċēaf, from Proto-West Germanic *skaub, from Proto-Germanic *skauba- (“sheaf”). === Pronunciation === enPR: shēf, IPA(key): /ʃiːf/ Rhymes: -iːf === Noun === sheaf (plural sheaves or sheafs) A quantity of the stalks and ears of wheat, rye, or other grain, bound together; a bundle of grain or straw. Synonyms: reap, wheatsheaf Any collection of things bound together. Synonym: bundle A bundle of arrows sufficient to fill a quiver, or the allowance of each archer. A quantity of arrows, usually twenty-four. (mechanics) A sheave. (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 F {\displaystyle {\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 } {\displaystyle \{U_{i}\}} of U {\displaystyle U} : If two sections over U {\displaystyle U} agree under restriction to every U i {\displaystyle U_{i}} , then the sections are the same. Given a family of sections s i ∈ F ( U i ) {\displaystyle s_{i}\in {\mathcal {F}}(U_{i})} such that all pairs ( s i , s j ) {\displaystyle (s_{i},s_{j})} agree under restriction to U i ∩ U j {\displaystyle U_{i}\cap U_{j}} , there is a (unique) section s {\displaystyle s} over U {\displaystyle U} whose restriction to U i {\displaystyle U_{i}} is s i {\displaystyle s_{i}} . ==== Derived terms ==== ==== Translations ==== === Verb === sheaf (third-person singular simple present sheafs, present participle sheafing, simple past and past participle sheafed) (transitive) To gather and bind into a sheaf; to make into sheaves (intransitive) To collect and bind cut grain, or the like; to make sheaves. === Anagrams === SFHEA, Shefa, SHAEF