2023/12/19 by Thomas Blom, Blom, Thomas, Ieke Moerdijk +1 · 1 citation
Mathematics · Medicine · #Homotopy and Cohomology in Algebraic Topology #Pituitary Gland Disorders and Treatments #Advanced Topics in Algebra
paper · pdf · doi:10.48550/arxiv.2312.12567
We show that the particular profinite completion used by Boavida-Horel-Robertson in their study of the Grothendieck-Teichmüller group fits in the framework of profinite completion as a left Quillen functor. More precisely, we construct a model category of profinite up-to-homotopy operads based on dendroidal objects in Quick's model category of profinite spaces and show that the construction of Boavida-Horel-Robertson extends to a left Quillen functor into this model category. We also characterize the underlying ∞-category of this model category and obtain a Dwyer-Kan style characterization of the weak equivalences between such profinite up-to-homotopy operads. Since this model category of profinite up-to-homotopy operads is Quillen equivalent to the one considered in our earlier paper "Profinite ∞-operads", we obtain analogous results in that setting.