We will continue online on Thursday, September 10, at 1pm on ZOOM platform (for information how to acces seminar and next programme visit this page) by the talk:

Edoardo Lanari (Czech Academy of Sciences)

Gray tensor products and lax functors of (∞,2)-categories

Abstract:
We give a definition of the Gray tensor product in the setting of scaled simplicial sets which is associative and forms a left Quillen bifunctor with respect to the bicategorical model structure of Lurie. We then introduce a notion of oplax functor in this setting, and use it in order to characterize the Gray tensor product by means of a universal property. A similar characterization was used by Gaitsgory and Rozenblyum in their definition of the Gray product, thus giving a promising lead for comparing the two settings.  This is a report on joint work with A. Gagna and Y. Harpaz.