Strictification of étale stacky Lie groups

摘要

AbstractWe define stacky Lie groups to be group objects in the 2-category of differentiable stacks. We show that every connected and étale stacky Lie group is equivalent to a crossed module of the form (Γ,G) where Γ is the fundamental group of the given stacky Lie group and G is the connected and simply connected Lie group integrating the Lie algebra of the stacky group. Our result is closely related to a strictification result of Baez and Lauda.