Polynomial monads and delooping of mapping spaces

Michael Batanin; Florian De Leger

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arXiv · 1712.00904

Polynomial monads and delooping of mapping spaces

Michael Batanin·Florian De Leger

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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.

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Michael Batanin, Florian De Leger. 2017-12-04. Polynomial monads and delooping of mapping spaces. https://arxiv.org/abs/1712.00904

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