nLab
étale infinity-groupoid

Idea

An étale ∞-groupoid is meant to be an ∞-groupoid-analog to an étale groupoid.

References

A formalization of the petit (∞,1)-toposes corresponding to étale ∞-groupoids is in

• Jacob Lurie, Structured Spaces.

A characterization of étale ∞-groupoids as objects in a big (∞,1)-topos is given in

• David Carchedi, Étale Stacks as Prolongations (arXiv:1212.2282)

and aspects of their geometric realization/shape modality are discussed in

• David Carchedi, On The Homotopy Type of Higher Orbifolds and Haefliger Classifying Spaces (arXiv:1504.02394)

A formalization in terms of differential cohesion is discussed at differential cohesion – Structures – cohesive étale ∞-groupoids.