Integrating morphisms of Lie 2-algebras

Abstract

We show how to integrate a weak morphism of Lie algebra crossed-modules to a weak morphism of Lie 2-groups. To do so we develop a theory of butterflies for 2-term L_infty algebras. In particular, we obtain a new description of the bicategory of 2-term L_infty algebras. We use butterflies to give a functorial construction of connected covers of Lie 2-groups. We also discuss the notion of homotopy fiber of a morphism of 2-term L_infty algebras.

discussion of connected covers of Lie 2-groups expanded, 26 pages

References in corpus (2)

• Integrating L-infinity algebras
• Butterflies I: morphisms of 2-group stacks

Cited by in corpus (6)

• Lie 2-algebras of vector fields
• Symmetric homotopy theory for operads
• Multiplicative vector fields on bundle gerbes
• On the homotopy theory for Lie $\infty$-groupoids, with an application to integrating $L_{\infty }$-algebras
• Explicit Non-Abelian Gerbes with Connections
• Gerbes in Geometry, Field Theory, and Quantisation