Homotopy nilpotent groups and their associated functors

Abstract

To every homotopy n-nilpotent group, defined in earlier work by Dwyer and the author, we associate an endofunctor of pointed spaces and prove that it is looped and n-excisive. As a tool we prove that $\Omega P_n(\mathrm{id})$ commutes with sifted colimits of connected spaces.

The author was asked to post this note for reference. We expect to expand on it in the near future. 7 pages