I have a problem with understanding Cohen's definition, as written in "The Homology of Iterated Loop Spaces" by Cohen, Lada and May (Part III, chapter 5, at the end of chapter).
So in order to define loop operations on a $n$-fold loop-suspension space $X$ in the vein of "A General Algebraic Approach to Steenrod Operations" I proceed as follows.
I have a little $n$-disks operad acting on $X$, so I have a map $D_n(r)\times_{\Sigma_r}X^r\to X$.
Out of this, I should derive a map of $\mathbb{Z}_p\pi$-complexes, where $\pi$ is cyclic of order $r$: $$ \theta :W^{(n)}\otimes C_*(X)^{\otimes r}\to C_*(X), $$ which is subject to the conditions described in "A General Algebraic Approach..." and allows me to define loop operations. Here $W^{(n)}$ is a $n$-th skeleton of a $\mathbb{Z}_p\pi$-free resolution of $\mathbb{Z}_p$.
In refered work, Cohen compute the cohomology of braid spaces. Then he takes the dual elements to the generators of image in $H^*(B\Sigma_r;\mathbb{Z}_p(q))$ and this allows him to define the loop operations.
So what I do not understand here is connection between points 3 and 2. Having all of Cohen's work done, how does it fit to "A General Algebraic Approach..." framework?
Sorry for any mistakes, I'm still a child in this area.
