September 22nd 2017; 12:00; Seminar room C3b/158
Joachim Kock, Infinity-operads as polynomial monads
Abstract: Lurie’s infinity-operads are defined as certain Gamma-spaces, in the spirit of May-Thomason.  A different approach to infinity-operads is due to Cisinski and Moerdijk in terms of dendroidal Segal spaces. After outlining these approaches, I will explain a new model for infinity-operads, given in terms of polynomial monads. This provides an infinity version of the classical viewpoint that operads are monoids in the monoidal category of species/analytic functors under the substitution product. Leaving out the technical details, I will explain the ideas behind the proof that the infinity-category of analytic monads is equivalent to the infinity-category of dendroidal Segal spaces.  This is joint work with David Gepner and Rune Haugseng.