Symmetric homotopy theory for operads

  title={Symmetric homotopy theory for operads},
  author={Malte Dehling and B. Vallette},
  journal={arXiv: Algebraic Topology},
The purpose of this foundational paper is to introduce various notions and constructions in order to develop the homotopy theory for differential graded operads over any ring. The main new idea is to consider the action of the symmetric groups as part of the defining structure of an operad and not as the underlying category. We introduce a new dual category of higher cooperads, a new higher bar-cobar adjunction with the category of operads, and a new higher notion of homotopy operads, for which… Expand
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