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Feb 15, 2012 at 5:15 comment added Mike Shulman Thanks, Justin! I've corrected the answer. I actually just heard Niles talk about your result (which I think is awesome by the way) at the JMM last month; I should have remembered it and mentioned it.
Feb 15, 2012 at 5:14 history edited Mike Shulman CC BY-SA 3.0
fixed A-infinity to E-infinity
Feb 14, 2012 at 9:25 comment added Ilias A. Mike, Noel, Thank you for your answers!
Feb 13, 2012 at 22:22 comment added Justin Noel @Mike: what you said is true if $T$ is the monad associated to an $E_\infty$ operad. In the $A_\infty$ case $Ho(T)$-algebras are homotopy associative H-spaces. Niles Johnson and I have worked out the obstruction theory in lifting a map of $Ho(T)$-algebras to a homotopy class of $T$-algebra maps (under appropriate restrictions) in a forthcoming paper.
Feb 13, 2012 at 20:32 history answered Mike Shulman CC BY-SA 3.0