nLab
simplicial operad

Contents

Definition

A simplicial operad is an operad over sSet. It has for each kk \in \mathbb{N} a simplicial set of kk-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

Classes of examples

Specific examples