Homotopy localizations with respect to arbitrary (possibly proper) classes of maps are known to existin 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 … Continue reading U. Haifa Topology & Geometry seminar: Tuesday, Jan. 9, 2024. Speaker: Carles Casacuberta (Barcelona). Title: “Homotopy reflectivity is equivalent to the weak Vopenka principle”.