Baez–Dolan Stabilization via (Semi-)Model Categories of Operads

We describe a proof of the Baez–Dolan Stabilization Hypothesis for Rezk’s model of weak n-categories. This proof proceeds via abstract homotopy theory, and en route we discuss a version of left Bousfield localization which does not require left properness. We also discuss conditions under which various categories of operads can be made left proper, but these conditions are difficult to be satisfied, as a counterexample in the context of simplicial sets demonstrates.