sheaf

Etymology
From, from , from , from.

Akin to 🇨🇬, 🇨🇬, 🇨🇬, 🇨🇬. Compare further 🇨🇬, 🇨🇬.

Noun

 * 1) A quantity of the stalks and ears of wheat, rye, or other grain, bound together; a bundle of grain or straw.
 * 2) Any collection of things bound together.
 * 3) A bundle of arrows sufficient to fill a quiver, or the allowance of each archer.
 * 4) A quantity of arrows, usually twenty-four.
 * 5)  A sheave.
 * 6)  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 $$U$$:
 * 7) If two sections over $$U$$ agree under restriction to every $$U_i$$, then the sections are the same.
 * 8) Given a family of sections $$s_i \in \mathcal{F}(U_i)$$ such that all pairs $$(s_i, s_j)$$ agree under restriction to $$U_i \cap U_j$$, there is a (unique) section $$s$$ over $$U$$ whose restriction to $$U_i$$ is $$s_i$$.
 * 1) A bundle of arrows sufficient to fill a quiver, or the allowance of each archer.
 * 2) A quantity of arrows, usually twenty-four.
 * 3)  A sheave.
 * 4)  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 $$U$$:
 * 5) If two sections over $$U$$ agree under restriction to every $$U_i$$, then the sections are the same.
 * 6) Given a family of sections $$s_i \in \mathcal{F}(U_i)$$ such that all pairs $$(s_i, s_j)$$ agree under restriction to $$U_i \cap U_j$$, there is a (unique) section $$s$$ over $$U$$ whose restriction to $$U_i$$ is $$s_i$$.
 * 1) If two sections over $$U$$ agree under restriction to every $$U_i$$, then the sections are the same.
 * 2) Given a family of sections $$s_i \in \mathcal{F}(U_i)$$ such that all pairs $$(s_i, s_j)$$ agree under restriction to $$U_i \cap U_j$$, there is a (unique) section $$s$$ over $$U$$ whose restriction to $$U_i$$ is $$s_i$$.

Translations

 * Arabic: حُزْمَة
 * Armenian:, , ,
 * Aromanian: mãnuclju
 * Belarusian: сноп, вяза́нка
 * Bulgarian:
 * Catalan:
 * Chinese:
 * Mandarin:
 * Chuvash: кӗлте
 * Czech:
 * Dalmatian: falja
 * Danish: neg
 * Dutch:
 * Esperanto: garbo
 * Faroese: bundi
 * Finnish:
 * French:
 * Galician:, , gavela,
 * Georgian: ძნა, კონა
 * German:
 * Greek:
 * Ancient: δράγμα, ἄμαλλα
 * Hungarian:
 * Ingrian: lyhe, vihko, kupo
 * Irish: punann
 * Italian: covone,, , , ,
 * Japanese:
 * Komi-Permyak: кольта
 * Korean:
 * Latgalian: kiuļs, snaps
 * Latin: merges, manipulus, garba
 * Latvian:
 * Macedonian: сноп
 * Marathi: पेंढी, पेंडी, भारा
 * Norwegian:
 * Persian:
 * Plautdietsch: Goaw
 * Polish:
 * Portuguese:
 * Romanian:, ,
 * Russian: ,
 * Scots: stook
 * Scottish Gaelic: sguab
 * Serbo-Croatian:
 * Cyrillic: сноп
 * Roman:
 * Slovak: snop
 * Slovene: snop
 * Sorbian:
 * Lower Sorbian: snop
 * Spanish:, , , ,
 * Swahili: mganda
 * Swedish:, sädeskärve
 * Udmurt: культо
 * Ukrainian: сніп,
 * Walloon:
 * Welsh:
 * Yiddish: גאַרב, סנאָפּ


 * Armenian:, ,
 * Bulgarian:
 * Catalan:
 * Chinese:
 * Mandarin:
 * Czech:
 * Dutch:
 * Finnish:
 * French: ,
 * German:
 * Greek:
 * Italian:, , ,
 * Maori: kākati
 * Marathi: भारा
 * Plautdietsch: Goaw
 * Portuguese: ,
 * Russian:, ,
 * Spanish: ,
 * Swedish:
 * Welsh: sypyn


 * Bulgarian:
 * Catalan:
 * Chinese:
 * Mandarin:
 * Danish:
 * Dutch:
 * Finnish:
 * French:
 * German:
 * Hungarian:
 * Italian:
 * Japanese:
 * Korean:
 * Norwegian: knippe
 * Portuguese:
 * Russian:
 * Serbo-Croatian:
 * Spanish:
 * Swedish:


 * Hebrew:
 * Korean: ,
 * Spanish:

Verb

 * 1)  To gather and bind into a sheaf; to make into sheaves
 * 2)  To collect and bind cut grain, or the like; to make sheaves.
 * 1)  To collect and bind cut grain, or the like; to make sheaves.