For $A$ an abelian group internal to CW-complexes, then $EA$ (constructed as a homotopy colimit over A with a point as a diagram) $BA$ (constructed as a quotient of $EA$ by its $A$-action).
It seems like $EA$ would have the structure of an abelian group, and that $BA$ does as well. My question is, is this a standard observation and can I find it somewhere in a textbook or journal?