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Especially in the context of sheaves on manifolds, sheaf cohomology can often be computed using resolutions by soft sheaves, fine sheaves, and flabby sheaves (also known as flasque sheaves from the French flasque meaning flabby). For example, a partition of unity argument shows that the sheaf of smooth functions on a manifold is soft.
Wheat sheaves near King's Somborne.Here the individual sheaves have been put together into a stook ("stooked") to dry. A sheaf of grain on a plaque Sheafing machine. A sheaf (/ ʃ iː f /; pl.: 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.
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 sheave or pulley wheel is a pulley using an axle supported by a frame or shell (block) to guide a cable or exert force.
In mathematics, a topos (US: / ˈ t ɒ p ɒ s /, UK: / ˈ t oʊ p oʊ s, ˈ t oʊ p ɒ s /; plural topoi / ˈ t ɒ p ɔɪ / or / ˈ t oʊ p ɔɪ /, or toposes) is a category that behaves like the category of sheaves of sets on a topological space (or more generally: on a site).
Sheaves is the plural of either of two nouns: Sheaf (disambiguation) Sheave This page was last edited on 1 October 2024, at 19:34 (UTC). Text is available under the ...
Wheat sheaves near King's Somborne, England arranged into a stook. Stooking maize in Kenya.. A stook /stʊk/, also referred to as a shock or stack, [1] is an arrangement of sheaves of cut grain-stalks placed so as to keep the grain-heads off the ground while still in the field and before collection for threshing.
The intuitive meaning of a stack is that it is a fibred category such that "all possible gluings work". The specification of gluings requires a definition of coverings with regard to which the gluings can be considered. It turns out that the general language for describing these coverings is that of a Grothendieck topology.
If dealing with sheaves of sets instead of sheaves of abelian groups, the same definition applies. Similarly, if f: (X, O X) → (Y, O Y) is a morphism of ringed spaces, we obtain a direct image functor f ∗: Sh(X,O X) → Sh(Y,O Y) from the category of sheaves of O X-modules to the category of sheaves of O Y-modules.