Polynomial monads and delooping of mapping spaces
Algebraic Topology
2020-01-16 v4 Algebraic Geometry
Category Theory
Abstract
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
@article{arxiv.1712.00904,
title = {Polynomial monads and delooping of mapping spaces},
author = {Michael Batanin and Florian De Leger},
journal= {arXiv preprint arXiv:1712.00904},
year = {2020}
}
Comments
This is the final version of the paper. The title has been changed