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1. • CommentRowNumber1.
   • CommentAuthorTim_Porter
   • CommentTimeFeb 16th 2013
   • PermaLink
   Author: Tim_Porter
   Format: MarkdownItexDoes anyone know if we have a discussion, somewhere, of the theorem of Thomason linking homotopy colimits with Grothendieck constructions. I have looked in places that I thought were likely but found no trace of it, but sometimes things get buried in entries on other topics so are difficult to find.

   Does anyone know if we have a discussion, somewhere, of the theorem of Thomason linking homotopy colimits with Grothendieck constructions. I have looked in places that I thought were likely but found no trace of it, but sometimes things get buried in entries on other topics so are difficult to find.

2. • CommentRowNumber2.
   • CommentAuthorTodd_Trimble
   • CommentTimeFeb 16th 2013
   • PermaLink
   Author: Todd_Trimble
   Format: MarkdownItex[This](http://ncatlab.org/nlab/show/geometric+realization+of+categories#behaviour_under_homotopy_colimits_39) may be what you're looking for.

   This may be what you’re looking for.

3. • CommentRowNumber3.
   • CommentAuthorTim_Porter
   • CommentTimeFeb 16th 2013
   • (edited Feb 16th 2013)
   • PermaLink
   Author: Tim_Porter
   Format: MarkdownItexThanks, Todd. That is almost it. In fact, I have seen an isomorphism quoted when the nerve is used without the geometric realisation. I found the paper is behind a paywall! I needed the statement to motivate a definition of hocolim for some notes (Grothendieck's construction had already been introduced) and I found the proof in Richard Lewis's thesis (i.e. my own student!;-)) Thanks again.

   Thanks, Todd. That is almost it. In fact, I have seen an isomorphism quoted when the nerve is used without the geometric realisation.

   I found the paper is behind a paywall! I needed the statement to motivate a definition of hocolim for some notes (Grothendieck’s construction had already been introduced) and I found the proof in Richard Lewis’s thesis (i.e. my own student!;-)) Thanks again.