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Jan 24, 2012 at 17:41 comment added Ronnie Brown Urs: Just a couple of points. 1) Strict structures have an advantage for the calculations we have in mind, in that one can for these usually work out how to calculate colimits. I am unsure how to make specific calculations with weak structures. 2) The last sentence of your answer is true only under certain conditions on the filtered space $X_*$ with total space $X$. See Section 14.7 of "Nonabelian algebraic topology". Our fundamental crossed complex and the associated higher homotopy groupoids, are defined only for filtered spaces.
Nov 7, 2009 at 6:37 vote accept Josh
Oct 27, 2009 at 7:30 comment added Urs Schreiber Sorry, I don't know why the first hyperlink spills over the next lines. It doesn't in the source code. It doesn't in the preview.
Oct 27, 2009 at 7:27 history answered Urs Schreiber CC BY-SA 2.5