Sheaf Cohomology Group
Sheaf may refer to: * Sheaf (agriculture), a bundle of harvested cereal stems * Sheaf (mathematics), a mathematical tool * Sheaf toss, a Scottish sport * River Sheaf, a tributary of River Don in England * ''The Sheaf'', a student-run newspaper serving the University of Saskatchewan * Aluma, a settlement in Israel whose name translates as ''Sheaf'' See also * Sceafa, a king of English legend * Sheath (other) * Sheave Sheave without a rope A pulley is a wheel on an axle or shaft enabling a taut cable or belt passing over the wheel to move and change direction, or transfer power between itself and a shaft. A pulley may have a groove or grooves between flan ...

Sheaf (agriculture)
A sheaf (; : sheaves) is a bunch of cereal-crop stems bound together after reaping, traditionally by sickle, later by scythe or, after its introduction in 1872, by a mechanical reaper-binder. Traditional hand-reapers, using scythes and working as a team, cut a field of grain clockwise, starting from an outside edge and finishing in the middle. Scything leaves a windrow of cut stems to the left of the reaper and, if cut skillfully, leaves the seed heads more or less aligned. These are then picked up and tied into sheaves by the sheavers, who traditionally use other cut stems as ties. These sheavers, or a following team, then stand the sheaves up in stooks to dry. Three to eight sheaves make up each stook, which forms a self-supporting A-frame with the grain-heads meeting at the top. This keeps the grain well ventilated, and off the ground allowing it to dry and discouraging vermin. The drying sheaves are later either placed by hand or pitched onto a cart. The traditional s ...
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Sheaf (mathematics)
In mathematics, a sheaf (: sheaves) is a tool for systematically tracking data (such as sets, abelian groups, rings) attached to the open sets of a topological space and defined locally with regard to them. For example, for each open set, the data could be the ring of continuous functions defined on that open set. Such data are well-behaved in that they can be restricted to smaller open sets, and also the data assigned to an open set are equivalent to all collections of compatible data assigned to collections of smaller open sets covering the original open set (intuitively, every datum is the sum of its constituent data). The field of mathematics that studies sheaves is called sheaf theory. Sheaves are understood conceptually as general and abstract objects. Their precise definition is rather technical. They are specifically defined as sheaves of sets or as sheaves of rings, for example, depending on the type of data assigned to the open sets. There are also maps (or ...
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