На этой странице Вы можете получить подробный анализ слова или словосочетания, произведенный с помощью лучшей на сегодняшний день технологии искусственного интеллекта:
математика
градуированный пучок
математика
градуированная алгебра
математика
градуированный модуль
математика
однородный идеал
математика
градуированное кольцо
математика
глобальное сечение
множественное число
от presheaf
математика
фактор-пучок
математика
пучок-небоскреб
математика
разделенный предпучок
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 for 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.