# Vocabulary Word

**Word:**sheaf

**Definition:**bundle of stalks of grain; any bundle of things tied together

## Sentences Containing 'sheaf'

A quasi-coherent sheaf is roughly one that looks locally like the sheaf of a module over a ring.

A semialgebraic function on "U" is defined to be a continuous real-valued function on "U" whose restriction to any semialgebraic set contained in "U" has a graph which is a semialgebraic subset of the product space R"n"×R. This endows R"n" with a sheaf formula_1 of semialgebraic functions.

A semialgebraic space is a locally ringed space formula_2 which is locally isomorphic to R"n" with its sheaf of semialgebraic functions.

A stack is called a stack in groupoids or a (2,1)-sheaf if it is also fibered in groupoids, meaning that its fibers (the inverse images of objects of "C") are groupoids.

An extension of "H" by "F" is a short exact sequence of sheaves
Note that an extension is not determined by the sheaf "G" alone: The morphisms are also important.

At that point most home matches switched to Bramall Lane, however Wednesday continued to play some games at Sheaf House until Olive Grove was opened in 1887.

But the placing of the cap-sheaf to all this blundering business was reserved for the scientific Frederick Cuvier, brother to the famous Baron.

Festival ceremonies entailed reenactment of mythological events or the performance of other symbolic acts, like the cutting of a sheaf of wheat during the harvest-related festival dedicated to the god Min.

He has won a Golden Sheaf Award for "Best Performance - Male" in "The Wager", and in 1999 he was nominated for a Gemini Award for "Best Performance by an Actor in a Featured Supporting Role in a Dramatic Series" for his work in "PSI Factor".

His book "Topologie Algébrique et Théorie des Faisceaux" from 1958 was, as he said, a very unoriginal idea for the time (that is, to write an exposition of sheaf theory); as a non-specialist, he managed to write an enduring classic.

His film "Uranium", the story of radioactive contamination on Native land by Canada's uranium mines, won a Golden Sheaf Award at the Yorkton Film Festival in 1991; "Power", a feature-length chronicle of the Cree's five-year struggle against the Great Whale Hydro Project in Northern Quebec, received the award for Best Documentary at the International Environmental Film Festival in Paris (1997), amongst other accolades and nominations.

In mathematics a stack or 2-sheaf is, roughly speaking, a sheaf that takes values in categories rather than sets.

In sheaf theory (an area of mathematics), a sheaf extension is a way of describing a sheaf in terms of a subsheaf and a quotient sheaf, analogous to a how a group extension describes a group in terms of a subgroup, and a quotient group.

In the case where "H" is the structure sheaf formula_5, we have formula_6, so the group of extensions of formula_7 by "F" is also isomorphic to the first sheaf cohomology group with coefficients in "F".

It was the work of Wailles of Newcastle upon Tyne and Spence of Montreal. In the left lights, a standing angel holds a scythe and a sheaf of wheat, symbolizing a life cut down.

More generally one can define the notion of an "n"-sheaf or "n"–1 stack, which is roughly a sort of sheaf taking values in "n"–1 categories.

Prior to the opening of the ground, Wednesday had used several other sites including Sheaf House and Bramall Lane, before newly formed rivals Sheffield United took up permanent residence there.

She also received the 1999 Golden Sheaf Award for her performance in the Genie Award winning film Moving Day.

Sheaf House is a former home ground of The Wednesday Football Club and was located near the centre of Sheffield, South Yorkshire, England.

Sheaf House was less suitable for hosting football matches than Bramall Lane (which was situated very close to the ground) but it was apparently cheaper to rent.

The category "c" is called a prestack over a category "C" with a Grothendieck topology if it is fibered over "C" and for any object "U" of "C" and objects "x", "y" of "c" with image "U", the functor from objects over "U" to sets taking "F":"V"→"U" to Hom("F"*"x","F"*"y") is a sheaf.

The ground has since been covered by a new development, however the Sheaf House pub which used to stand at the corner of the ground is still there.

The left light displays a sheaf of lilies, a symbol of the Resurrection.

This means that constructing the pullback of a quasicoherent sheaf under a morphism of stacks requires some extra effort.

Two sites were proposed for the development - Carbrook, in the North East of the city, and Owlerton, then a rural area to the North West; an alternative was a return to Sheaf House.

Wednesday then moved again to Sheaf House.

# More Vocab Words

::: perigee - point of moon's orbit when it is nearest the earth; CF. apogee::: parallelism - state of being parallel; similarity; analogy

::: veracious - (of a person) truthful

::: volition - act of using one's will; act of making a conscious choice; Ex. She selected this dress of her own volition.

::: hoary - white with age

::: bullion - gold and silver in the form of bars

::: indifferent - unmoved or unconcerned by; having no interest in; mediocre; neither good nor bad

::: perennial - something long-lasting; perennial plant; ADJ: lasting through the year or many years; lasting for a long time; enduring

::: sidetrack - switch (a railroad car) to a siding; divert from a main issue; N. CF. siding: short section of railroad track connected by switches with a main track

::: titular - of a title; in name only; nominal; having the title of an office without the obligations; Ex. titular head of the company