Free products of higher operad algebras

Mark Weber

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.

TAC Home