Algebras of Higher Operads as Enriched Categories

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Algebras of Higher Operads as Enriched Categories
Abstract. One of the open problems in higher category theory is the systematic construction of the higher dimensional analogues of the Gray tensor product. In this paper we begin to adapt the machinery of globular operads [1] to this task. We present a general construction of a tensor product on the category of n-globular sets from any normalised (n + 1)-operad A, in such a way that the algebras for A may be recaptured as enriched categories for the induced tensor product. This is an important step in reconciling the globular and simplicial approaches to higher category theory, because in the simplicial approaches one proceeds inductively following the idea that a weak (n + 1)category is something like a category enriched in weak n-categories. In this paper we reveal how such an intuition may be formulated in terms of globular operads.
Michael Batanin, Mark Weber
Added 28 May 2011
Updated 28 May 2011
Type Journal
Year 2011
Where ACS
Authors Michael Batanin, Mark Weber
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