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.
Keywords: operads, higher categories, funny tensor product
2010 MSC: 18A05, 18D20, 18D50, 55P48
Theory and Applications of Categories, Vol. 28, 2013, No. 2, pp 24-65.
Published 2013-01-25.
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