  We 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 (\`a 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.
