nLab
generalized (infinity,1)-operad

Contents

Contents

Idea

An ordinary (∞,1)-operad 𝒪\mathcal{O} is equivalently incarnated as its (∞,1)-category of operators 𝒪 FinSet *\mathcal{O}^\otimes \to FinSet_*, which in particular has the property that 𝒪 0 *\mathcal{O}^{\otimes}_{\langle 0\rangle} \simeq *.

A generalized (,1)(\infty,1)-operad is like an (∞,1)-category of operators only that this condition is dropped and

𝒞𝒪 0 \mathcal{C} \coloneqq \mathcal{O}^{\otimes}_{\langle 0\rangle}

is allowed to be any (∞,1)-category.

It is essentially the same kind of data as a family of (∞,1)-operads (see there for more) parameterized over 𝒞\mathcal{C}.

References

Section 2.3.2 of

Created on February 11, 2013 at 19:31:33. See the history of this page for a list of all contributions to it.