Spahn étale types (Rev #2, changes)

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Π inf\mathbf{\Pi}_inf-closed morphisms

Definition (Π inf\mathbf{\Pi}_inf-closed morphism)
Definition (Π inf\mathbf{\Pi}_inf-closed object)
Theorem (Formally étale subslices are coreflecive)

Models

Étale groupoids

Theorem (Classical étale groupoids)
Theorem (Formally étale \infty-groupoids are étale simplicial manifolds)

\infty-orbifolds

Definition (\infty-orbifold)
Theorem (De Rham theorem for \infty-orbifolds)
Observation (Inertia \infty-orbifold)

UU-modelled higher manifolds

Theorem (Hausdorff manifold)

(1) XX is a paracompact if there is a set of monomorphisms ϕ i: nX\phi_i:\mathbb{R}^n\to X such that the corresponding Cech groupoid ζ ϕ\zeta_\phi is degree-wise a coproduct of copies of n\mathbb{R}^n.

(2) XX is hausdorff if ζ ϕ\zeta_\phi is moreover étale.

Definition (UU-modelled \infty-manifold)

Revision on December 3, 2012 at 13:51:43 by Stephan Alexander Spahn?. See the history of this page for a list of all contributions to it.