Ben Walter and I make the functors $\Gamma$ and $A$ more explicit, by using an explicit model for the cofree Lie Coalgebra functor, in this paperthis paper. We do not discuss the application to $\infty$-algebras as Bruno does in much greater generality. (We were interested in using explicit models to be able to compute, in particular in the long exact sequence of a fibration as we do in a sequel to this paper on Hopf invariants.)