perhaps relevant is the recent developments of bar constructions for operads cf the special case of going fromt he dg Lie operad to the L_\infty operad ************************************************************ Until August 10, 1998, I am on leave from UNC and am at the University of Pennsylvania Jim Stasheff jds@math.upenn.edu 146 Woodland Dr Lansdale PA 19446 (215)822-6707 Jim Stasheff jds@math.unc.edu Math-UNC (919)-962-9607 Chapel Hill NC FAX:(919)-962-2568 27599-3250 On Tue, 18 Nov 1997, categories wrote:

Date: Mon, 17 Nov 1997 16:07:01 -0800 (PST) From: john baez <baez@math.ucr.edu>

In their book "Homotopy invariant structures on topological structures", Boardman and Vogt construct from any topological operad O a new one WO, which can be thought of as a "weakened" version of O in which all the laws of O now hold only up to homotopy in a coherent way.

Has there been any subsequent work clarifying this construction? Here I'm not interested so much in all the *other* approaches to infinite loop space machines, as in the notion of "weakening" a topological operad. For example, Boardman and Vogt point out that their construction can be used to discuss homotopy colimits, which makes me wonder if the construction of WO from O could be done slickly using homotopy colimits. Has anyone discussed this?

Best, John Baez