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Sheaf (mathematics)

In mathematics, a sheaf (pl.: 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…

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Sheaf cohomology

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Sheaf (mathematics)

Nodes241
Edges240
Triples7
Avg. degree1.99
Density0.008299
Components1

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Important terminology

displaystyle sheaf sheaves open mathcal cohomology space sections theory topological functions set sets complex presheaf spaces example category also groups

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
that of a differentiable manifold or a scheme can be expressed in terms of a sheaf of rings on the spaceinstance ofgeometric structures0.80text
vector bundles or divisors are naturally specified in terms of sheavesinstance ofseveral geometric constructions0.80text
singular cohomologyinstance oftopological cohomology theories0.80text
sheaf cohomology since an intersection theory can be built using these kinds of sheaves from the Serre intersection formulainstance ofThis kind of formalism was found to be extremely powerful and motivates a lot of homological algebra0.80text
mathematical analysisinstance ofIt is still common in some areas of mathematics0.80text
the derived categoryinstance ofAdvanced techniques0.80text
vanishing cycles on the most reasonable spacesinstance ofAdvanced techniques0.80text

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