A G-coefficient system valued in $\mathcal{C}$ is a functor $\mathcal{O}_G^{op} \rightarrow \mathcal{C}$.

Examples

A version of Elmendorf's theorem states that the $\infty$-category of G-spaces is equivalent to $G$-coefficient systems in the $\infty$-category $\mathcal{S}$ of spaces.

Mackey functors have underlying coefficient systems, given by pullback along the embedding $\mathcal{O}_G^{\op} \hookrightarrow \mathbb{F}_G^{\op} \hookrightarrow \mathrm{Span}(\mathbb{F}_G)$, the latter inclusion being the wide subcategory of backwards maps.

Created on July 30, 2024 at 15:28:41.
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