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.
Keywords: operads, polynomial monads, delooping
2020 MSC: 18M65, 55P48
Theory and Applications of Categories, Vol. 45, 2026, No. 27, pp 1117-1146.
Published 2026-05-13.
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