### Context

#### Higher algebra

higher algebra

universal algebra

# Contents

## Definition

A simplicial operad is an operad over sSet. It has for each $k\in ℕ$ a simplicial set of $k$-ary operations.

## Structures on the category of simplicial operads

### Model structure

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.

## Examples

### Specific examples

• The Barratt-Eccles operad has, as a simplicial operad, a single color, and its simplicial set of $n$-ary operations is the nerve $N\left({\Sigma }_{n}//{\Sigma }_{n}\right)$ of the action groupoid ${\Sigma }_{n}//{\Sigma }_{n}$ of the symmetric group ${\Sigma }_{n}$ acting on itself. This is a contractible simplicial set in each degree, and, indeed, this operad is a resolution of Comm, which has the point in each degree.

Revised on March 7, 2012 02:13:29 by Urs Schreiber (82.169.65.155)