(2,1)-quasitopos?
structures in a cohesive (∞,1)-topos
An étale ∞-groupoid is meant to be an ∞-groupoid-analog to an étale groupoid.
For details see at V-manifold.
classifying étale stack for symplectic forms: Carchedi 12, Example 2
classifying étale stack for complex structures: Carchedi 12, p. 38
A formalization of the petit (∞,1)-toposes corresponding to étale ∞-groupoids is in
A characterization of étale ∞-groupoids as objects in a big (∞,1)-topos is given in
David Carchedi, Étale Stacks as Prolongations, Advances in Mathematics Volume 352, 20 August 2019, Pages 56-132 (arXiv:1212.2282)
David Carchedi, Higher Orbifolds and Deligne-Mumford Stacks as Structured Infinity-Topoi, Memoirs of the American Mathematical Society 2020; 120 (arXiv:1312.2204, ISBN:978-1-4704-5810-2)
and aspects of their geometric realization/shape modality are discussed in
David Carchedi, On The Homotopy Type of Higher Orbifolds and Haefliger Classifying Spaces, Advances of Mathematics, Volume 294, 2016, Pages 756-818 (arXiv:1504.02394)
David Carchedi, On the étale homotopy type of higher stacks (arXiv:1511.07830)
A formalization as V-manifolds in terms of differential cohesion is discussed at differential cohesion – Structures – cohesive étale ∞-groupoids.
The formalization of this in homotopy type theory is discussed in
Last revised on July 13, 2020 at 09:40:34. See the history of this page for a list of all contributions to it.