Subject: "weakened" operads

From: categories <[email-masked]>
Date: Tue, 18 Nov 1997 21:11:24 -0400 (AST)

Date: Mon, 17 Nov 1997 16:07:01 -0800 (PST)
From: john baez <[email-masked]>

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

---

From: categories <[email-masked]>
Date: Thu, 20 Nov 1997 15:51:23 -0400 (AST)

Date: Thu, 20 Nov 1997 14:02:49 -0500 (EST)
From: James Stasheff <[email-masked]>

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		[email-masked]

	146 Woodland Dr
        Lansdale PA 19446       (215)822-6707	

	Jim Stasheff		[email-masked]
	Math-UNC		(919)-962-9607
	Chapel Hill NC		FAX:(919)-962-2568
	27599-3250