Eduard Czech Institute Workshop talk: Colimit preservation from weaker large cardinals

Andrew D Brooke-Taylor (Speaker)

Activity: Participating in or organising an event typesInvited talk

Description

Eduard Czech Institute Workshop talk: Colimit preservation from weaker large cardinals

Abstract: An old theorem of Rosicky, Trnkova and Adamek states that, under the assumption of Vopenka's Principle, any full embedding into an accessible category preserves sufficiently directed colimits, and in fact this statement is equivalent to Vopenka's Principle. In joint work with Joan Bagaria, we have shown that for a given embedding, the large cardinal assumption required can be weakened, calibrated by the definition complexity of the embedding and its domain category. We also have an almost level-by-level equivalence, being able to obtain back almost as much large cardinal strength from these embedding statements.
Period24 Oct 2014
Event typeWorkshop

Keywords

  • set theory
  • category theory