nLab generalized (infinity,1)-operad




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}.


Section 2.3.2 of

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