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Higher categorified algebras versus bounded homotopy algebras
Theory and applications of categories, Tome 25 (2011), pp. 251-275
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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.

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Classification : 18D05, 55U15, 17B70, 18D10, 18G30
Keywords: Higher category, homotopy algebra, monoidal category, Eilenberg-Zilber map 
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David Khudaverdyan; Ashis Mandal; Norbert Poncin. Higher categorified algebras versus bounded homotopy algebras. Theory and applications of categories, Tome 25 (2011), pp. 251-275. http://geodesic.mathdoc.fr/item/TAC_2011_25_a9/