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We show that general relativity can be viewed as a higher gauge theory involving a categorical group, or 2-group, called the teleparallel 2-group.
1923
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R. Debever, Élie Cartan and Albert Einstein: Letters on Absolute Parallelism, 1929–1932
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J. Baez and A. Crans, Higher dimensional algebra VI: Lie 2-algebras, Theory Appl. of Categ
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J. Baez and A. Lauda, Higher dimensional algebra V: 2-groups, Theory Appl. Categ
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L. Breen and W. Messing, Differential geometry of gerbes, Adv. Math
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L. Crane and D. N. Yetter, Measurable categories and 2-groups, Appl. Categor. Struct
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K. C. H. Mackenzie, General Theory of Lie Groupoids and Lie Algebroids
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D. Yetter, Measurable categories, Appl. Cat. Str
2005
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T. Sauer, Field equations in teleparallel spacetime: Einstein’s Fernparallelismus
2006
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J. Baez, A. Crans, U. Schreiber and D. Stevenson From loop groups to 2-groups, HHA
2007
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J. Baez and U. Schreiber, Higher gauge theory, in Categories in Algebra, Geometry and Mathematical Physics
2007
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2009
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D. K. Wise, Symmetric space Cartan connections and gravity in three and four dimensions, SIGMA
2009
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D. K. Wise, MacDowell–Mansouri gravity and Cartan geometry, Class. Quant. Grav
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J. Baez and J. Huerta, An invitation to higher gauge theory, Gen. Relat. Gravit
2011
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K. Behrend and P. Xu, Differentiable stacks and gerbes, J. Symplectic Geom
2011
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D. Roytenberg, On weak Lie 2-algebras, AIP Conf. Proc
2007
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2008
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L. Freidel and K. Krasnov, A new spin foam model for 4d gravity, Class. Quant. Grav
2008
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2008
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A. Henriques, Integrating L ∞ L_{\infty} -algebras, Compositio Math
2008
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A. Baratin and D. Wise, 2-Group representations for spin foams, AIP Conf. Proc
2009
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J. F. Martins and R. Picken, On two-dimensional holonomy, Trans. Amer. Math. Soc
2011
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2011
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J. Baez, A. Baratin, L. Freidel and D. Wise, Infinite-Dimensional Representations of 2-Groups
2012
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A. Miković and M. Vojinović, Poincaré 2-group and quantum gravity, Class. Quant. Grav
2012
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R. Aldrovandi and J. G. Pereira, Teleparallel Gravity: an Introduction
2013
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A. Baratin and L. Freidel, Hidden quantum gravity in 4d Feynman diagrams: emergence of spin foams, Class. Quant. Grav
2060
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