**Title**: Left proper model structures on algebras over colored operads**Speaker**: David White, Denison**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 so that the resulting model structure on P-algebras is left proper. We'll apply this machinery to 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 left proper model structures from M in the presence of this axiom and the hypothesis of h-monoidality. The primary application of this work is a proof due to Michael Batanin of the Baez-Dolan Stabilization Hypothesis.

# Topology Seminar - David White

Tuesday, March 31, 2015 - 3:00pm to 4:00pm

CH240