A Lie characterization of the Bousfield-Kan $\mathbb{Q}$-completion and $\mathbb{Q}$-good spaces

Abstract

We prove that the unit of the Quillen pair $\mathfrak{L}:\mathbf{sset}\rightleftarrows \mathbf{cdgl}:⟨\cdot ⟩$ given by the model and realization functor is, up to homotopy, the Bousfield-Kan $\mathbb{Q}$-completion.

Major revision in this version according to the accurate referee's corrections and suggestions