  The aim of this paper is to study convergence of Bousfield-Kan completions
with respect to the 1-excisive approximation of the identity functor and exotic
convergence of the Taylor tower of the identity functor, for algebras over
operads in spectra centered away from the null object. In Goodwillie's homotopy
functor calculus, being centered away from the null object amounts to doing
homotopy theory and functor calculus in the retractive setting.
