nLab topological operad

Definition

A topological operad is an operad over Top. It has for each $k \in \mathbb{N}$ a topological space of $k$-ary operations.

Model structure

There is a model category structure on the category of topological operads that makes them present (∞,1)-operads. See model structure on operads.

Examples

• Every operad over Set may be regarded as a topological operad, via the discrete space embedding $Disc : Set \to Top$.

• the little k-cubes operad is naturally a topological operad

Related concepts

• topological operad, simplicial operad

• dg-operad