We define Lie 3-algebras and prove that these are in 1-to-1 correspondence with the 3-term Lie infinity algebras whose bilinear and trilinear maps vanish in degree (1,1) and in total degree 1, respectively. Further, we give an answer to a question of Roytenberg pertaining to the use of the nerve and normalization functors in the study of the relationship between categorified algebras and truncated sh algebras.
Keywords: Higher category, homotopy algebra, monoidal category, Eilenberg-Zilber map
2000 MSC: 18D05, 55U15, 17B70, 18D10, 18G30
Theory and Applications of Categories, Vol. 25, 2011, No. 10, pp 251-275.
Published 2011-06-17.
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