Integrating morphisms of Lie 2-algebras

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.