From: "vitia-t" Date: Tue, 18 Jul 2006 11:27:33 +0400 (MSD) Is it well known that the homotopy totalization of a cosimplicial space commutes with the suspension (under some mild conditions)? I have a sketch of the proof from Tom Goodwillie, but I wonder whether it was already known. Probably in general the homotopy totalization commutes with homotopy colimits?