
TL;DR
This paper develops a new framework using butterflies for 2-term L_infty algebras to integrate morphisms of Lie 2-algebras into Lie 2-groups, providing a functorial approach to connected covers.
Contribution
It introduces butterflies for 2-term L_infty algebras and uses them to integrate morphisms into Lie 2-groups, offering a new perspective on the bicategory structure.
Findings
New description of the bicategory of 2-term L_infty algebras
Functorial construction of connected covers of Lie 2-groups
Analysis of homotopy fiber of morphisms in 2-term L_infty 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.
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