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Algebra over an operad : ウィキペディア英語版
Algebra over an operad
In algebra, given an operad ''O'' (a symmetric sequence in a symmetric monoidal ∞-category ''C''), an algebra over an operad, or ''O''-algebra for short, is, roughly, a left module over ''O'' with multiplications parametrized by ''O''.
If ''O'' is a topological operad, then one can say an algebra over an operad is an ''O''-monoid object in ''C''. If ''C'' is symmetric monoidal, this recovers the usual definition.
Let ''C'' be symmetric monoidal ∞-category with monoidal structure distributive over colimits. If f: O \to O' is a map of operads and, moreover, if ''f'' is a homotopy equivalence, then the ∞-category of algebras over ''O'' in ''C'' is equivalent to the ∞-category of algebras over ''O in ''C''.
== See also ==

*En-ring
*Homotopy Lie algebra

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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