nLab G-symmetric sequence

Idea

G-symmetric sequences are to symmetric sequences as G-∞-operads are to (∞,1)-operads.

Definition

Let $\underline{\Sigma}_G$ be the fiberwise core of the $G$-$\infty$-category $\mathbb{F}_G$ of finite G-sets, and let $\mathrm{tot}\underline{\Sigma}_G$ be the total $\infty$-category of the corresponding of the corresponding cocartesian fibration.

Definition

A $G$-symmetric sequence is a functor $\mathrm{tot}\underline{\Sigma}_G \rightarrow \mathcal{S}$.

Properties

(..)

Related concepts

• Parametrized Higher Category Theory and Higher Algebra

• G-operad

References

• Natalie Stewart: On tensor products of equivariant commutative operads (draft) [pdf]