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Algebras of higher operads as enriched categories II

Authors
  • Batanin, Michael
  • Cisinski, Denis-Charles
  • Weber, Mark
Type
Preprint
Publication Date
Apr 20, 2010
Submission Date
Sep 25, 2009
Identifiers
arXiv ID: 0909.4715
Source
arXiv
License
Yellow
External links

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 continue the work of [7] to adapt the machinery of globular operads [4] to this task. The resulting theory includes the Gray tensor product of 2-categories and the Crans tensor product [12] of Gray categories. Moreover much of the previous work on the globular approach to higher category theory is simplified by our new foundations, and we illustrate this by giving an expedited account of many aspects of Cheng's analysis [11] of Trimble's definition of weak n-category. By way of application we obtain an "Ekmann-Hilton" result for braided monoidal 2-categories, and give the construction of a tensor product of A-infinity algebras.

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