Kan replacement of simplicial manifolds

Abstract

We establish a functor $Kan$ from local Kan simplicial manifolds to weak Kan simplicial manifolds. It gives a solution to the problem of extending local Lie groupoids to Lie 2-groupoids.

19 pages, 11 figures, Lemma 2.2 improved, Prop.-Def. 2.3 modified. to appear in Letters in Mathematical Physics

References in corpus (5)

• Higher Topos Theory
• Integrating L-infinity algebras
• L_infinity algebras as 1-jets of simplicial manifolds (and a bit beyond)
• Lie n-groupoids and stacky Lie groupoids
• Lie II theorem for Lie algebroids via higher groupoids

Cited by in corpus (8)

• From double Lie groupoids to local Lie 2-groupoids
• Higher Groupoid Bundles, Higher Spaces, and Self-Dual Tensor Field Equations
• Integration of Exact Courant Algebroids
• Symplectic structures on the integration of exact Courant algebroids
• Constant Symplectic 2-groupoids
• Strictification of etale stacky Lie groups
• Transitive Courant algebroids and double symplectic groupoids
• Differentiating $L_{\infty }$ groupoids