Definitions for sheafʃif

This page provides all possible meanings and translations of the word sheaf

Princeton's WordNetRate this definition:(0.00 / 0 votes)

  1. bundle, sheaf(noun)

    a package of several things tied together for carrying or storing

WiktionaryRate this definition:(0.00 / 0 votes)

  1. sheaf(Noun)

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

  2. sheaf(Noun)

    Any collection of things bound together; a bundle.

    a sheaf of paper

  3. sheaf(Noun)

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

  4. sheaf(Noun)

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

  5. sheaf(Noun)

    (mechanical) A sheave.

  6. sheaf(Noun)

    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. sheaf(Verb)

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

  8. sheaf(Verb)

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

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

Webster DictionaryRate this definition:(0.00 / 0 votes)

  1. Sheaf(noun)

    a sheave

  2. Sheaf(noun)

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

  3. Sheaf(noun)

    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. Sheaf(verb)

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

  5. Sheaf(verb)

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

  6. Origin: [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.]

FreebaseRate this definition:(0.00 / 0 votes)

  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.


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