nLab G-d-operad

Idea

$G$-$d$-operads are to G-∞-operads as d-operads are to ∞-operads.

Definition

Definition

Fix $d \in \mathbb{N}$ a natural number A $G$-$\infty$-operad $\mathcal{O}^{\otimes}$ is essentially $d$ (or a $G$-$d$-operad) if, for all colors $X_1,\dots,X_n,Y \in U\mathcal{O}$, the space $\mathrm{Mul}_{\mathcal{O}}(X_1,\dots,X_n;Y)$ is $(d-1)$-truncated

Related concepts

• Parametrized Higher Category Theory and Higher Algebra

• G-∞ operads / N-∞ operads

References

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