Bicat is not triequivalent to Gray

Steve Lack – 13 December 2006

I'll talk a bit in general about tricategories and Gray-categories. I'll also talk about a recent paper with the same name as the talk. There is a tricategory Bicat of bicategories, homomorphisms, pseudonatural transformations, and modifications, and a subtricategory Gray consisting of only the 2-categories and the 2-functors, with all pseudonatural transformations and modifications between them. In the paper I show that these two tricategories are not triequivalent.