Cofinal morphism of polynomial monads and double delooping
Algebraic Topology
2025-08-19 v2 Category Theory
Abstract
Using the theory of internal algebras classifiers developed by Batanin and Berger, we construct a morphism of polynomial monads which we prove is homotopically cofinal. We then describe how this result constitutes the main conceptual argument for a categorical direct double delooping proof of the Turchin-Dwyer-Hess theorem concerning the explicit double delooping of spaces of long knots.
Cite
@article{arxiv.2205.09149,
title = {Cofinal morphism of polynomial monads and double delooping},
author = {Florian De Leger},
journal= {arXiv preprint arXiv:2205.09149},
year = {2025}
}