## EVENT DETAILS AND ABSTRACT

**Topology Seminar**
**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.

**Date:** Monday, March 26, 2012

**Time:** 3:00pm

**Where:** Lunt 10

**Contact Person:** Prof. Paul Goerss

**Contact email:** pgoerss@math.northwestern.edu

**Contact Phone:** 847-491-8544

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