Activity: Participating in or organising an event types › Invited talk

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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.