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The goal of this short paper is to study the convergence of the Taylor towerof the identity functor in the context of operadic algebras in spectra.Specifically, we show that if $A$ is a $(-1)$-connected $\mathcal{O}$-algebrawith $0$-connected $\mathsf{TQ}$-homology spectrum $\mathsf{TQ}(A)$, then thereis a natural weak equivalence $P_\infty$(id)$A\simeq A_\mathsf{TQ}^\wedge$between the limit of the Taylor tower of the identity functor evaluated on $A$and the $\mathsf{TQ}$-completion of $A$. Since, in this context, the identityfunctor is only known to be $0$-analytic, this result extends knowledge of theTaylor tower of the identity beyond its "radius of convergence."

TQ-completion and the Taylor tower of the identity functor