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In mathematics, an -algebra in a symmetric monoidal infinity category ''C'' consists of the following data: *An object for any open subset ''U'' of Rn homeomorphic to an ''n''-disk. *A multiplication map: *: :for any disjoint open disks contained in some open disk ''V'' subject to the requirements that the multiplication maps are compatible with composition, and that is an equivalence if . An equivalent definition is that ''A'' is an algebra in ''C'' over the little ''n''-disks operad. == Examples == * An -algebra in vector spaces over a field is a unital associative algebra if ''n''=1, and a unital commutative associative algebra if ''n''≥2. * An -algebra in categories is a monoidal category if ''n''=1, a braided monoidal category if ''n''=2, and a symmetric monoidal category if ''n''≥3. * If Λ is a commutative ring, then defines an -algebra in the infinity category of chain complexes of -modules. 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「En-ring」の詳細全文を読む スポンサード リンク
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