We will describe work in preparation on coloured operads, acting via correspondances on Map(N,M) for N,M manifolds exhibiting suitable topological conditions.

Monoids are to categories what operads are to coloured operads, and what we propose to put forth in this talk could be considered a 'colourification' of the spineless cacti operad. The main immediate advantage of this approach is that the situation easily generalizes to give spectral actions on higher free loop spaces; Map(S^n,M). For n=1, this is -- up to homotopy -- the Cohen-Jones construction of the Chas-Sullivan loop product. We will describe why N=S^n provides the best statements and how we -- in this case -- have an acting coloured operad, intimately related to E_{n+1}-operads; in the sense that they are disjoint union of coloured colour-contractible E_{n+1}-operads.