Nicola di Vittorio – 2 June 2021

Introduced independently by Grothendieck and Heller in the 1980s, derivators provide a formal way to study homotopy theories by working in some quotient of them. In the last few years, Riehl and Verity have been establishing the theory of ∞-cosmoi, particular (∞, 2)-categories where one can develop (∞, 1)-category theory. They noticed that much of the theory of ∞-cosmoi could be developed inside a quotient, the homotopy 2-category. In this talk I will introduce a 2-categorical notion of derivator that formalizes these ideas. This is joint work with Dominic Verity.