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E∞-operad
In the theory of operads in algebra and algebraic topology, an E∞-operad is a parameter space for a multiplication map that is associative and commutative "up to all higher homotopies. (An operad that describes a multiplication that is associative but not necessarily commutative "up to homotopy" is called an A∞-operad.)
== Definition ==
For the definition, it is necessary to work in the category of operads with an action of the symmetric group. An operad ''A'' is said to be an E∞-operad if all of its spaces ''E''(''n'') are contractible; some authors also require the action of the symmetric group Σ''n'' on ''E''(''n'') to be free. In other categories than topological spaces, the notion of ''contractibility'' has to be replaced by suitable analogs, such as acyclicity in the category of chain complexes.
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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