Funny tensor products

Mark Weber – 11 November 2009

One of the central pen problems of higher category theory is to describe the higher dimensional analogues of the Gray tensor product of 2-categories, as part of an inductive machine that would provide a definition of "semi-strict n-category". If we ignore al information on 2-cells in the Gray tensor product on 2-Cat, we get a well-known product on Cat. This is frequently called the "funny tensor product". In this talk I'll explain why the funny tensor product is a very general phenomenon: there is an analogous tensor product for any higher dimensional structure definable by a "normalized" n-operad in the sense of Batanin.