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7 votes

Pullbacks of classifying spaces

On the other hand, if we define $BG$ by the usual simplicial construction, then the functor $B$ does indeed preserve pullbacks. Indeed, if we start with a pullback square $(G,H,J,K)$ then in the ...
Neil Strickland's user avatar
10 votes

Pullbacks of classifying spaces

This is not true. Note that $BG$ is only well-defined up to homotopy equivalence, so the only question that makes sense is when the square $$\begin{array}{ccc} B\big(G \underset H\times H'\big) & \...
R. van Dobben de Bruyn's user avatar
0 votes

Classifying space of a non-discrete group and relationship between group homology and topological homology of Lie groups

For future record, since my post question seems already kinda messy, I will document something new in this answer and leave the question itself untouched. The following is trying to answer my question ...
XYC's user avatar
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