Kan replacement of simplicial manifolds

TL;DR

This paper introduces a functor called Kan that transforms local Kan simplicial manifolds into weak Kan simplicial manifolds, addressing the extension of local Lie groupoids to Lie 2-groupoids.

Contribution

It provides a novel functorial method to extend local Lie groupoids to higher structures, specifically Lie 2-groupoids.

Findings

Established a functor from local Kan to weak Kan simplicial manifolds

Solved the problem of extending local Lie groupoids to Lie 2-groupoids

Contributed to higher Lie groupoid theory

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.