I am reading lecture notes on topology and the total space $E(U(N))$ is given as a geometric realization of a simplicial space $$E(U(N))=|[n]\rightarrow U(N)^{n+1}|$$ Here I am confused because
1) the details about face and degeneracy maps are missing. What are they exactly?
2) I am confused that left handside depends on $n$ and right handside does not. Is it correct that I should have written $$E(U(N))=|[n]\rightarrow U(N)^{n+1}|$$ whatever that means. Probably, I wasn't careful to take the notes in the class. Wikipedia and ncatlab provide the simplicial space for the $BG$ and they give the special case for $EU$ geometrically without explaining the face/degeneracy maps.