## On tensor product of A_{\infty}-categories, E_n-algebras and higher categories

### Michael Batanin – 27 May 2009

The problem of the right generalisation of Gray-tensor product is notoriously hard. In homotopy theory an analogous status is achieved by the problem of definition of a tensor product of A_{\infty}-categories (or A_{\infty}-algebras). Tensor product of E_n-algebras is even more mysterious.
In my (not always formal) talk I'll try to suggest a general method for constructing such tensor products based on our joint work with Cisinski and Weber on multitensors.

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