2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/222696We describe the Koszul dual of two quadratic operads on planar forests introduced to study the infinitesimal Hopf algebra of planar rooted trees and prove that these operads are Koszul.18 pagesRings and Algebras05C05; 18D50text