nLab module over an operad


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.


  • 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.

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