  We define, for a somewhat standard forgetful functor from nonsymmetric
operads to weight graded associative algebras, two functorial "enveloping
operad" functors, the right inverse and the left adjoint of the forgetful
functor. Those functors turn out to be related by operadic Koszul duality, and
that relationship can be utilised to provide examples showing limitations of
two standard tools of the Koszul duality theory. We also apply these functors
to get a homotopical algebra proof of the Lagrange inversion formula.
