From: Rainer Vogt <Rainer.Vogt@mathematik.Uni-Osnabrueck.DE>
Date: Wed, 13 Jan 1999 12:12:13 +0100 (MET)
Subject: Re: nerve of covering


Let D be the diagram of the spaces U_ij and their intersectios with maps
being the inclusions. You first prove that the homotopy colimit hocolim D
is homotopy equivalent to M = colim D. Since the spaces in D are contractible
hocolim D is homotopy equivalent to hocolim D' where D' is obtained from D
by replacing each space by a singleton. But hocolim D' is the nerve of the
covering.

Rainer Vogt