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

Aniceto Murillo; Mario Fuentes; Yves F\'elix

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

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arxiv 2407.02812 v2 pith:W4HR4I2R submitted 2024-07-03 math.AT

Yves Félix , Mario Fuentes , Aniceto Murillo This is my paper · ORCID

classification math.AT

keywords mathbbbousfield-kancoloncompletioncdglcdotcharacterizationfunctor

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abstract

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

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A new approach to rational stable parametrized homotopy theory
math.AT 2025-09 conditional novelty 6.0 of 10

Rational parametrized spectra over a (connected) base are claimed equivalent, as a monoidal category, to differential graded modules over the completed enveloping algebra of a Lie model of the base.

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