I am wondering how one should think of the higher stacks $B^n(G)$?
Here is what I mean: The stack $BG$ can be thought of as the quotient of a point by the group $G$ ($BG = */G$) in the proper category. It can also be represented by a groupoid $G \rightrightarrows *$. I would like to know if same sort of thing is true for the higher $B^n(G)$? For example it is presumably the case that I can think of $B^2 G$ as a 2-groupoid with a single object, a single morphism, and the group $G$ as the 2-morphisms (however by a Eckmann–Hilton sort of argument this would require $G$ to be abelian). In the case that $G$ is abelian can I then say that $BG$ is a group object in the category of stacks and that $B^{2}G = */BG$? If $G$ is not abelian then how is $B^nG$ even defined?