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.
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Acknowledgments
We thank the referee very much for very helpful comments. Both authors give their warmest thanks to Courant Research Centre “Higher Order Structures”, Göttingen University, and Jilin University, where this work was done during their visits.
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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.
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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Sheng, Y., Zhu, C. Integration of Lie 2-Algebras and Their Morphisms. Lett Math Phys 102, 223–244 (2012). https://doi.org/10.1007/s11005-012-0578-1
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DOI: https://doi.org/10.1007/s11005-012-0578-1