Bonn Topology Group - Abstracts

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CHRIS SCHOMMER-PRIES (MPI): The Unicity of the homotopy theory of higher categories


This talk will describe joint work with Clark Barwick, which addresses the comparison problem in higher category theory. We show that a simple axiomatization (just 4 axioms!) characterizes the homotopy theory of (infinity, n)-categories up to equivalence and, moreover, that the space on theories satisfying these axioms is B(Z/2)^n. This generalizes a theorem Toen when n=1, an it verifies two conjectures of Simpson. We also provide a large class of examples satisfying our axioms, including those of Joyal, Kan, Lurie, Rezk, and Simpson.

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