Integration of Lie 2-algebras and their morphisms

Abstract

Given a strict Lie 2-algebra, we can integrate it to a strict Lie 2-group by integrating the corresponding Lie algebra crossed module. On the other hand, the integration procedure of Getzler and Henriques will also produce a 2-group. In this paper, we show that these two integration results are Morita equivalent. As an application, we integrate a non-strict morphism between Lie algebra crossed modules to a generalized morphism between their corresponding Lie group crossed modules.

19 pages, Lett. Math. Phys. 102 (2), (2012.11), 223-244

References in corpus (2)

• From double Lie groupoids to local Lie 2-groupoids
• Non-abelian Extensions of Lie 2-algebras

Cited by in corpus (7)

• Semistrict Higher Gauge Theory
• Higher Groupoid Bundles, Higher Spaces, and Self-Dual Tensor Field Equations
• Higher Gauge Theory
• A cohomological proof for the integrability of strict Lie 2-algebras
• A cohomology theory for Lie 2-algebras
• Cohomology of hemistrict Lie 2-algebras
• Non-abelian Extensions of Lie algebras with derivations