nLab infinity-permutation representation

Idea

An ∞-representation on objects of ∞Grpd.

The analog on (∞,1)-category theory of a permutation representation.

Properties

Tannaka duality

See at Tannaka duality the section For ∞-permutation representations.

Grothendieck construction

By the (∞,1)-Grothendieck construction $\infty$-permutation representations

$$\mathbf{B}G \to \infty \mathrm{Grpd}$$

correspond to ∞-functors

$$V//G \to \mathbf{B}G$$

sitting in fiber sequences

$$V \to V//G \to \mathbf{B}G \,,$$

where $V//G$ is the corresponding action ∞-groupoid?.