, Volume 102, Issue 2, pp 223-244,
Open Access This content is freely available online to anyone, anywhere at any time.
Date: 28 Jul 2012

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.

Y. Sheng is supported by NSFC (11101179) and SRFDP (20100061120096). C. Zhu is supported by the German Research Foundation (Deutsche Forschungsgemeinschaft (DFG)) through the Institutional Strategy of the University of Göttingen.