Hi, am looking to fill a gap in the nLab entry on realization of simplicial spaces:

What's good sufficient conditions on a square of simplicial spaces, which is degreewise a homotopy pullback, for its geometric realization to be a homotopy pullback square?

I am looking at Anderson 1978 projecteuclid.org/journals/… but find it hard to extract the gist:

From page 2 there I gather that a sufficient condition is: One of the morphisms of simplicial spaces is (a) a Kan fibration on connected components, and (b) such that each component space of both domain and codomain is discrete or connected.

Is that the right reading? (It certainly seems to be what it says on that p. 2, but it seems to require work to see where this is proven.) Is there a more modern reference for this?

Thanks!

does anyone know where to find a copy of Hirsch, "quelques propriétés des produits de steenrod"? This is the original reference for the Hirsch formula (ab) cup_1 c = a(b cup_1 c) + (-1)^{|b||c|+|b|} (a cup_1 c) b in my preferred sign conventions. I'm curious what else is in this paper.