2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/163486We introduce the operad Moor, dual of the operad NAP and the notion of Moor-bialgebras. We warn the reader that the compatibility relation linking the Moor-operation with the Moor-cooperation is not distributive in the sense of Loday. Nevertheless, a rigidity theorem (à la Hopf-Borel) for the category of connected Moor-bialgebras is given. We show also that free permutative algebras can be equipped with a Moor-cooperation whose compatibility with the permutative product looks like the infinitesimal relation.V2. Radical change of the paperQuantum AlgebraRings and Algebras16D99, 16W30, 17A30text