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started an entry on the Borel construction, indicating its relation to the nerve of the action groupoid.
That is very useful and very ’timely’ as I was looking for a good reference for the Borel construction and orbifolds. :-)
added a subsection called
As a homotopy colimit over the category associated to $G$
This entry was lacking a decent reference. I have taken the liberty now of pointing to
Please feel invited to add you favorite classical textbook account on the Borel construction, instead (which is?)
added mentioning of the simplicial version and some lines (here) relating to the model structure on simplicial group actions
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