What do DG-categories form? (after Tamarkin)

Michael Batanin – 26 July 2006

It is classical that DG-categories, DG-functors and and their complex of natural transformations can be organised in a DG-enriched 2-category. But in practice it is much more important to consider the derived complex of natural transformations between DG-functors. In a recent preprint Tamarkin showed that there is a "homotopy" 2-category structure on this enriched 2-graph. Precisely, he exhibited an action of a contractible 2-operad on this 2-graph. In this talk we will give an overview of Tamarkin's paper and also will show how it is related to the works of Berger/Fress, McClure/Smith and Kotsevich/Soibelman on Deligne's conjecture, Street/Day's work on convolution structure in lax monoidal categories and Batanin's work on symmetrisation of n-operads. This is joint work with Clemens Berger.