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.

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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