David White
Dennison University
Title
The Baez-Dolan Stabilization Hypothesis for various models of weak n-categories
Abstract
In 1995, Baez and Dolan hypothesized that any good model for weak n-categories should satisfy a stability result for k-tuply monoidal weak n-categories. I will report on recent joint work with Michael Batanin in which we prove such a stabilization theorem for a wide variety of models of weak n-categories (arxiv:2001.05432, 2001.03764) including Rezk’s Theta_n spaces, Tamsamani’s model, Simpson’s Segal n-categories, Ara’s n-quasi-categories, Bergner-Rezk mdoels based on (complete) Segal spaces and more. We model k-tuply monoidal weak n-categories as algebras over a k-operad, then work out the homotopy theory of such objects, then prove that stabilization (from k-tuply monoidal to (k+1)-tuply monoidal, in a stable range of n) is a Quillen equivalence. The proof involves model structures, Bousfield localization, and homotopical Beck-Chevalley squares, but I’ll try to de-emphasize such technicalities.
