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What are layers of the Goodwillie tower of the functor "n-th iterated loop space" from based spaces to based spaces? I know the answer for n=0.

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    $\begingroup$ As $\Omega^n$ preserves homotopy pullbacks, the derivatives of $\Omega^n$ will just be $\Omega^n$ of the derivatives of the identity. $\endgroup$
    – Neil Strickland
    Commented Oct 3, 2014 at 11:47
  • $\begingroup$ @NeilStrickland Thank you very much, Neil! It was pretty obvious, I am ashamed. In fact, I am looking for a functor, whose Goodwillie tower looks like the one for identity, but the Lie operad is replaced with the (suspension spectrum of) little cubes operad. $\endgroup$
    – nikitamarkarian
    Commented Oct 4, 2014 at 8:03

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