  In my Montreal lecture notes of 1988, it was suggested that the theory of
linear quantum groups can be presented in the framework of the category of {\it
quadratic algebras} (imagined as algebras of functions on "quantum linear
spaces"), and quadratic algebras of their inner (co)homomorphisms.
  Soon it was understood (E. Getzler and J. Jones, V. Ginzburg, M. Kapranov, M.
Kontsevich, M. Markl, B. Vallette et al.) that the class of {\it quadratic
operads} can be introduced and the main theorems about quadratic algebras can
be generalised to the level of such operads, if their components are {\it
linear spaces} (or objects of more general monoidal categories.)
  When quantum cohomology entered the scene, it turned out that the basic tree
level (genus zero) (co)operad of quantum cohomology not only is {\it quadratic}
one, but its {\it components are themselves quadratic algebras.}
  In this short note, I am studying the interaction of quadratic algebras
structure with operadic structure in the context of enriched category formalism
due to G. M. Kelly et al.
