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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