symmetric monoidal (∞,1)-category of spectra
A simplicial operad is an operad over sSet. It has for each $k \in \mathbb{N}$ a simplicial set of $k$-ary operations.
There is a model category structure on the category of simplicial operads that makes them present (∞,1)-operads. See model structure on operads.
There is a Quillen equivalence between this model structure and the model structure on dendroidal sets, via the dendroidal homotopy coherent nerve.
Every operad over Set may be regarded as a simplicial operad, via the discrete object embedding $Disc : Set \to sSet$.
Every topological operad induces a simplicial operad by applying the singular simplicial complex functor $Sing : Top \to sSet$ degreewise.
Every dendroidal set induces a simplicial operad via the right adjoint to the dendroidal homotopy coherent nerve.
Last revised on March 7, 2012 at 02:13:29. See the history of this page for a list of all contributions to it.