We extend some classical results – such as Quillen’s Theorem A, the Grothendieck construction, Thomason’s theorem and the characterisation of homotopically cofinal functors – from the homotopy theory of small categories to polynomial monads and their algebras.
As an application we give a categorical proof of the Dwyer–Hess and Turchin results concerning the explicit double delooping of spaces of long knots.
Cite this article
Michael A. Batanin, Florian De Leger, Polynomial monads and delooping of mapping spaces. J. Noncommut. Geom. 13 (2019), no. 4, pp. 1521–1576DOI 10.4171/JNCG/355