What does sheaf mean?

Definitions for sheaf
ʃifsheaf

This dictionary definitions page includes all the possible meanings, example usage and translations of the word sheaf.

Princeton's WordNet

  1. bundle, sheafnoun

    a package of several things tied together for carrying or storing

Wiktionary

  1. sheafnoun

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

  2. sheafnoun

    Any collection of things bound together; a bundle.

    a sheaf of paper

  3. sheafnoun

    A bundle of arrows sufficient to fill a quiver, or the allowance of each archer.

  4. sheafnoun

    (unit) A quantity of arrows, usually twenty-four.

  5. sheafnoun

    (mechanical) A sheave.

  6. sheafnoun

    An abstract construct in topology that associates data to the open sets of a topological space, together with well-defined restrictions from larger to smaller open sets, subject to the condition that compatible data on overlapping open sets corresponds, via the restrictions, to a unique datum on the union of the open sets.

  7. sheafverb

    To gather and bind into a sheaf; to make into sheaves; as, to sheaf wheat.

  8. sheafverb

    To collect and bind cut grain, or the like; to make sheaves.

  9. Etymology: sceaf, from. Akin to German Schaub, Old Norse skauf. Compare Gothic 0343033A033F03460344, German Schopf, Albanian çup.

Samuel Johnson's Dictionary

  1. Sheafnoun

    sheaves plural.

    Etymology: seaf , Saxon; schoof, Dutch.

    These be the sheaves that honour’s harvest bears,
    The seed thy valiant acts, the world the field. Edward Fairfax.

    He beheld a field,
    Part arable and tilth; whereon were sheaves
    New-reap’d: the other part sheep-walks and folds. John Milton.

    The reaper fills his greedy hands,
    And binds the golden sheaves in brittle bands. Dryden.

    I pitch’d the sheaves (oh could I do so now)
    Which she in rows pil’d. John Gay, Pastorals.

    She vanish’d;
    The sheaf of arrows shook and rattled in the case. Dryden.

    In the knowledge of bodies, we must glean what we can; since we cannot, from a discovery of their real essences, grasp at a time whole sheaves; and in bundles comprehend the nature of whole species. John Locke.

ChatGPT

  1. sheaf

    In mathematics, specifically in algebraic geometry and related areas, a sheaf is a tool for systematically tracking locally defined data attached to the open sets of a topological space. The data can be thought of as sections of a bundle over the space. The key property of sheaves is that they can "glue" data defined on overlapping open sets. More formally, a sheaf F over a topological space X is a contravariant functor from the category of open sets in X to the category of sets (or abelian groups, or modules, etc.) which satisfies the following conditions: 1. For every open cover {Ui} of an open set U in X, if s is a section over U, and s restricts to the same section over each intersection Ui ∩ Uj for all i, j, then s must restrict to the same section over each Ui. 2. For every open cover {Ui} of U, if a section si over each Ui restricts to the same section over each intersection Ui ∩ Uj for all i, j, then there is a unique section s over U that restricts to each si over Ui. These two properties are referred to as locality and gluing, respectively. Sheaves allow us to make precise the intuitive idea of defining geometric or algebraic objects locally, and then patching these local pieces together to obtain a global object.

Webster Dictionary

  1. Sheafnoun

    a sheave

  2. Sheafnoun

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

  3. Sheafnoun

    any collection of things bound together; a bundle; specifically, a bundle of arrows sufficient to fill a quiver, or the allowance of each archer, -- usually twenty-four

  4. Sheafverb

    to gather and bind into a sheaf; to make into sheaves; as, to sheaf wheat

  5. Sheafverb

    to collect and bind cut grain, or the like; to make sheaves

  6. Etymology: [OE. sheef, shef, schef, AS. scef; akin to D. schoof, OHG. scoub, G. schaub, Icel. skauf a fox's brush, and E. shove. See Shove.]

Wikidata

  1. Sheaf

    In mathematics, a sheaf is a tool for systematically tracking locally defined data attached to the open sets of a topological space. The data can be restricted to smaller open sets, and the data assigned to an open set is equivalent to all collections of compatible data assigned to collections of smaller open sets covering the original one. For example, such data can consist of the rings of continuous or smooth real-valued functions defined on each open set. Sheaves are by design quite general and abstract objects, and their correct definition is rather technical. They exist in several varieties such as sheaves of sets or sheaves of rings, depending on the type of data assigned to open sets. There are also maps from one sheaf to another; sheaves with their morphisms on a fixed topological space form a category. On the other hand, to each continuous map there is associated both a direct image functor, taking sheaves and their morphisms on the domain to sheaves and morphisms on the codomain, and an inverse image functor operating in the opposite direction. These functors, and certain variants of theirs, are essential parts of sheaf theory.

Chambers 20th Century Dictionary

  1. Sheaf

    shēf, n. a quantity of things, esp. the stalks of grain, put together and bound: a bundle of arrows, usually 24 in number: any bundle or collection:—pl. Sheaves (shēvz).—v.t. to bind in sheaves.—v.i. to make sheaves.—adj. Sheaf′y. [A.S. sceáf—A.S. scúfan, to shove; Ger. schaub, Dut. schoof.]

Dictionary of Nautical Terms

  1. sheaf

    A bundle of arrows, as formerly supplied to our royal ships.

Military Dictionary and Gazetteer

  1. sheaf

    A bundle of arrows.

Surnames Frequency by Census Records

  1. SHEAF

    According to the U.S. Census Bureau, Sheaf is ranked #142108 in terms of the most common surnames in America.

    The Sheaf surname appeared 117 times in the 2010 census and if you were to sample 100,000 people in the United States, approximately 0 would have the surname Sheaf.

    94.8% or 111 total occurrences were White.
    4.2% or 5 total occurrences were of Hispanic origin.

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Numerology

  1. Chaldean Numerology

    The numerical value of sheaf in Chaldean Numerology is: 4

  2. Pythagorean Numerology

    The numerical value of sheaf in Pythagorean Numerology is: 3

Popularity rank by frequency of use

sheaf#10000#58252#100000

Translations for sheaf

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"sheaf." Definitions.net. STANDS4 LLC, 2024. Web. 12 Jul 2024. <https://www.definitions.net/definition/sheaf>.

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