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Free products of higher operad algebras
Theory and applications of categories, Tome 28 (2013), pp. 24-65
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One of the open problems in higher category theory is the systematic construction of the higher dimensional analogues of the Gray tensor product of 2-categories. In this paper we continue the developments of [Batanin-Weber, 2011], [Weber, 2011] and [Batanin-Cisinski-Weber, 2011] by understanding the natural generalisations of Gray's little brother, the funny tensor product of categories. In fact we exhibit for any higher categorical structure definable by a normalised n-operad in the sense of Batanin, an analogous tensor product which forms a symmetric monoidal closed structure on the category of algebras of the operad.

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Classification : 18A05, 18D20, 18D50, 55P48
Keywords: operads, higher categories, funny tensor product 
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     author = {Mark Weber},
     title = {Free products of higher operad algebras},
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     volume = {28},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2013_28_a1/}
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Mark Weber. Free products of higher operad algebras. Theory and applications of categories, Tome 28 (2013), pp. 24-65. http://geodesic.mathdoc.fr/item/TAC_2013_28_a1/