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Operadic twisting as an adjunction
Guillaume Laplante-Anfossi, Adrian Petr, Vivek Shende
https://arxiv.org/abs/2510.02229 https://arxiv.org/pdf/2510.02229

Operadic twisting as an adjunction
For operads with a map from the curved homotopy Lie operad, we introduce a corresponding curved variant `cTw' of Willwacher's operadic twisting comonad `Tw'. We show that cTw-coalgebra structures on such an operad are in bijection with certain splittings (not respecting the differential) of the projection to its quotient by the curvature operation. We derive a similar classification of Tw-coalgebras. For the class of operads whose Koszul dual admits a unital extension, we give explicit formul…