Dear category theorists, I have been plagued by the following question: does the classifying space functor commute with (co)limits? In particular, I have a system of compact topological groups G_i indexed by the natural numbers, and a whole lot of inclusions. Is B colim G_i homotopic to colim BG_i ? I have a hint that this should be so in my particular situation (in a letter of Serre to Grothendieck), but I'd like to know how the general case goes. Cheers, ------------------------------------------------------------------------ -- David Roberts School of Mathematical Sciences University of Adelaide SA 5005 ------------------------------------------------------------------------ -- droberts@maths.adelaide.edu.au www.maths.adelaide.edu.au/~droberts www.trf.org.au