Algebra/Topology seminar

Speaker: David White

Title: Left Proper Model Structures on algebras over operads and the Baez-Dolan Stabilization Hypothesis

Abstract:  We will recall the usual method, introduced by Schwede and Shipley, of transferring a model structure on a monoidal model category M to the category of P-algebras where P is a colored operad. We'll then discuss what hypotheses are needed on M in order for this to work for the situations where P is a cofibrant colored operad, when P is the commutative monoid operad, and when P is the colored operad for non-reduced operads. We introduce the commutative monoid axiom and prove that the latter two situations inherit model structures from M in the presence of this axiom. We then include a discussion of when P-alg is left proper, and an application to proving the Baez-Dolan Stabilization Hypothesis.