E) of the operad Mo. 7). Let us consider the moduli space N(n) of Riemann spheres with n + 1 decorated marked points, where a decoration is a choice of a real tangent direction at the marked point. In phyzspeak, these decorations are called `phase parameters' at the point.

A E-module A is represented by a sequence of objects, {A([n])},,,>1 in C with a right on A([n]). We will use the notation A(n) in place of A([n]). May's original definition of an operad [May72] was for the category of topolog- ical spaces, with compactly generated topology, but it generalizes with a few minor assumptions to an arbitrary symmetric monoidal category C with multiplication denoted by O. 7 we will reformulate the definition for Setf-modules, but it is simpler to begin with a definition for E-modules.