Algebra/Topology Seminar

Speaker: Michael Batanin

Title: Grothendieck homotopy theory for polynomial monads

Abstract: Grothendieck homotopy theory of small categories can be considered as a theory of ∞-groupoids but it has a strong combinatorial flavour very useful in numerous applications.The goal of my talk is to show that many fundamental constructions of Grothendieck homotopy theory can be extended from small categories to finitary polynomial monads and their algebras.This includes Grothendieck construction, Quillen theorem A, algebraic homotopy Kan extensions and the theory of homotopy cofinal morphisms. If time permits I will mention an application of this technique to delooping of spaces of long knots (joint work with Florian De Leger).