|
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 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）』 ■ウィキペディアで「algebra over an operad」の詳細全文を読む スポンサード リンク
|