Re: "weakened" operads

Re: "weakened" operads

[categories]

Date: Thu, 20 Nov 1997 14:02:49 -0500 (EST)
From: James Stasheff <jds@math.upenn.edu>

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

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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
> 
> 
> 

"weakened" operads

[categories]

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