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1. • CommentRowNumber1.
   • CommentAuthorDmitri Pavlov
   • CommentTimeJul 30th 2021
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexCreated: ## Definition An [[operad]] is a [[monoid]] in the [[monoidal category]] of [[symmetric sequences]] equipped with the [[substitution product]]. A __module over an operad__ is just a [[right module]] over this [[monoid]]. Right modules are very different from left modules, the latter are essentially [[algebras over an operad]]. ## Related concepts * [[operad]] * [[algebra over an operad]] * [[module over an algebra over an operad]] ## References * [[V. A. Smirnov]]. ON THE COCHAIN COMPLEX OF TOPOLOGICAL SPACES. Mathematics of the USSR-Sbornik 43:1 (1982), 133–144. [doi](http://dx.doi.org/10.1070/sm1982v043n01abeh002437). * [[Martin Markl]], _Models for operads_, Comm. Algebra 24 (1996), no. 4, 1471–1500. [arXiv:hep-th/9411208v1](https://arxiv.org/abs/hep-th/9411208v1). <a href="https://ncatlab.org/nlab/revision/module+over+an+operad/1">v1</a>, <a href="https://ncatlab.org/nlab/show/module+over+an+operad">current</a>

   Created:

   Definition

   An operad is a monoid in the monoidal category of symmetric sequences equipped with the substitution product.

   A module over an operad is just a right module over this monoid.

   Right modules are very different from left modules, the latter are essentially algebras over an operad.

   Related concepts

   • operad

   • algebra over an operad

   • module over an algebra over an operad

   References

   • V. A. Smirnov. ON THE COCHAIN COMPLEX OF TOPOLOGICAL SPACES. Mathematics of the USSR-Sbornik 43:1 (1982), 133–144. doi.

   • Martin Markl, Models for operads, Comm. Algebra 24 (1996), no. 4, 1471–1500. arXiv:hep-th/9411208v1.

   v1, current