nLab G-commutative monoid

Definition

Definition

If $\mathcal{C}$ is a G-∞-category, then the $G$-$\infty$-category of $G$-commutative monoid objects in $\mathcal{C}$ is

$$\underline{\mathrm{CMon}}_G := \underline{\mathrm{Fun}}_G(\mathrm{Span}(\mathbb{F}_G),\mathcal{C}),$$

where $\mathrm{Span}(\mathbb{F}_G)$ is the category of correspondences in finite G-sets.

Related concepts

• Mackey functor

• equivariant symmetric monoidal category

• algebraic pattern

References

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