U. Haifa Topology & Geometry seminar: Tuesday, Jan. 9, 2024. Speaker: Carles Casacuberta (Barcelona). Title: “Homotopy reflectivity is equivalent to the weak Vopenka principle”.
Homotopy localizations with respect to arbitrary (possibly proper) classes of maps are known to exist
in suitably structured model categories assuming the validity of Vopenka’s principle from set theory.
Through recent progress in large cardinal theory, we prove that the existence of localization with respect
to every class of maps in the homotopy category of simplicial sets or spectra is in fact equivalent to the
so-called weak Vopenka principle.
This is joint work with Javier Gutierrez.
Zoom recording:
