Title: Barwick and Schommer-Pries's Unicity Axioms
Abstract: We sketch out some of the ideas behind Barwick and Schommer-Pries's unicity axioms for the ∞-category of (∞,n)-categories for 1<n<∞. In this talk, we will try to give some motivations including some examples beyond the cobordism hypothesis. Next, we will try to emphasize the more geometric, algebraic, or homotopical aspects, in particular invoking topological intuition when possible, and try to keep the combinatorics to a minimum (or really gloss over a large amount of content in general). No knowledge of higher category theory should be required so long as one is willing to take some basic ∞-categorical results for granted. Time permitting, we may discuss an extension of the unicity axioms to d-Cartesian fibrations, how to get a description of the ∞-equipment of (∞,n)-categories, and something resembling an internal language of the latter.
