Content

Idea

A $G$-$\infty$-operad is an $\mathcal{N}_\infty$-operad if it is infinitely connected, unital, and prescribes binary multiplications on fixed points for all subgroups.

These are meant to model the equivariant commutative operads which contain a non-genuine version of $\mathbb{E}_\infty$.

Related concepts

• Parametrized Higher Category Theory and Higher Algebra

• equivariant symmetric monoidal category, G-∞-operad

• algebraic pattern

References

Originally,

• Andrew Blumberg, Michael Hill, Operadic multiplications in equivariant spectra, norms, and transfers, (arXiv:1309.1750)

Classification via indexing systems (each independently proves this):

• Jonathan Rubin, Combinatorial $N_\infty$ operads (2017), (arXiv:1705.03585)

• Javier Gutiérrez, David White, Encoding Equivariant Commutativity via Operads (2017), (arXiv:1707.02130)

• Peter Bonventre, Luis Pereira, Genuine equivariant operads, (2017) (1707.02226)

• Denis Nardin, Jay Shah, Parametrized and equivariant higher algebra, (2022) (arxiv:2203.00072)

Presentation of algebras in the $C_p$-equivariant case:

• Lucy Yang, On normed $\mathbb{E}_\infty$-rings in genuine equivariant $C_p$-spectra, (2023) (arXiv:2308.16107)