Injective Sheaf
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High Quality Content by WIKIPEDIA articles! In mathematics, injective sheaves of abelian groups are used to construct the resolutions needed to define sheaf cohomology (and other derived functors, such as sheaf Ext.). There is a further group of related concepts applied to sheaves: flabby (flasque in French), fine, soft (mou in French), acyclic. In the history of the subject they were introduced before the 1957 'Tohoku' paper of Alexander Grothendieck, which showed that the abelian category notion of injective object sufficed to found the theory. The other classes of sheaves are historically older notions. The abstract framework of defining cohomology and derived functors does not need them. However, in most concrete situations, resolutions by acyclic sheaves are often easier to construct. Acyclic sheaves therefore serve for computational purposes, for example the Leray spectral sequence.
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GarantieWeitere Informationen
- Allgemeine Informationen
- GTIN 09786131200748
- Editor Lambert M. Surhone, Miriam T. Timpledon, Susan F. Marseken
- EAN 9786131200748
- Format Fachbuch
- Titel Injective Sheaf
- Herausgeber Betascript Publishing
- Anzahl Seiten 100
- Genre Mathematik
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