Matan Prasma: Homotopy normal maps

A map of loop spaces is called homotopy normal if the homotopy quotient caries a loop space structure, compatible with the quotient map. In this talk we will characterize homotopy normal maps via  coherent group actions and show that they are invariant under weakly monoidal endofunctors of spaces. As a result, we deduce that localization by a map preserves principal fibrations.