So, I'm trying to fill up the details in some of the propositions of Goerss and Jardine's book, "Simplicial Homotopy Theory". On Lemma 7.6, I've tried to do something similar to what we do in the case of topological spaces (usually using stuff about $H$-spaces), but I'm having trouble describing the second multiplication $\star$ mentioned in the proof.
Any help would be appreciated.
Thanks in advance.