Subject: 2 ?? rational homotopy theory
From: jim stasheff <jds@math.upenn.edu>
Date: Fri, 09 Mar 2007 11:00:08 -0500

A_\infty or L_\infty algebras or morphisms can be described the old 
fashioned way in 
terms of component maps V^\otimes n \to V or via a coderivation D of 
square 0
on the bar construction or the analog for Lie

homotopies of such morphisms are given as coderivation homotopies on the 
bar construction or the analog for Lie
or via the Quillen version using V[t,dt]

Is it written anywhere how these homotopies look in terms of component 
maps??

Has anyone looked at non-commutative rational homotopy theory?
aka `quantum'  rational homotopy theory?


jim stasheff