Subject: categories: classifying functor and colimits

From: David Roberts <[email-masked]>
Date: Thu, 24 Aug 2006 15:29:15 +0930

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,

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David Roberts
School of Mathematical Sciences
University of Adelaide SA 5005
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[email-masked]
www.maths.adelaide.edu.au/~droberts
www.trf.org.au