Sheaf

English

Etymology

From Template:Inh, from Template:Inh, from Template:Inh, from Template:Der.

Template:Col-top Akin to Template:Cog, Template:Cog, Template:Cog, Template:Cog. Compare further Template:Cog, Template:Cog. Template:Col-bottom

Pronunciation

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Sheaves

Noun

1. Template:SenseidA quantity of the stalks and ears of wheat, rye, or other grain, bound together; a bundle of grain or straw.

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2. Any collection of things bound together.

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3. A bundle of arrows sufficient to fill a quiver, or the allowance of each archer.
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4. A quantity of arrows, usually twenty-four.
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5. Template:Lb A sheave.
6. Template:Lb 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 $U$:
   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 $s_i\in ℱ(U_i)$ 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

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Verb

1. Template:Lb To gather and bind into a sheaf; to make into sheaves

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2. Template:Lb To collect and bind cut grain, or the like; to make sheaves.
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Anagrams

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