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In mathematics, Grothendieck's six operations, named after Alexander Grothendieck, is a formalism in homological algebra. It originally sprang from the relations in étale cohomology that arise from a morphism of schemes . The basic insight was that many of the elementary facts relating cohomology on ''X'' and ''Y'' were formal consequences of a small number of axioms. These axioms hold in many cases completely unrelated to the original context, and therefore the formal consequences also hold. The six operations formalism has since been shown to apply to contexts such as ''D''-modules on algebraic varieties, sheaves on locally compact topological spaces, and motives. == The operations == The operations are six functors. Usually these are functors between derived categories and so are actually left and right derived functors. * the inverse image * the direct image * the proper (or extraordinary) direct image * the proper (or extraordinary) inverse image * internal tensor product * internal Hom The functors and form an adjoint functor pair, as do and . Similarly, internal tensor product is left adjoint to internal Hom. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「six operations」の詳細全文を読む スポンサード リンク
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