EVENT DETAILS AND ABSTRACT

Title: On the unicity of the homotopy theory of higher categories.
Speaker: Chris Schommer-Pries
Speaker Info: MIT
Brief Description:
Special Note: This is an unusual time and place.
Abstract:

We will discuss joint work with Clark Barwick in which we propose four axioms that a quasicategory should satisfy to be considered a reasonable homotopy theory of $(\infty, n)$-categories. This axiomatization requires that a homotopy theory of $(\infty, n)$-categories, when equipped with a small amount of extra structure, satisfies a simple, yet surprising, universal property. We further prove that the space of such quasicategories is homotopy equivalent to B(Z/2)^n. This generalizes a theorem of Toen when n = 1, and it verifies two conjectures of Simpson. In particular, any two such quasicategories are equivalent. We also provide a large class of examples of models satisfying our axioms, including those of Joyal, Kan, Lurie, Simpson, and Rezk.