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Elementary embeddings for category theory

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If you have a question about this talk, please contact Tamara von Glehn.

Elementary embeddings do crop up in category theory, but are often viewed as being simply convenient morphisms of the category in question. In set theory much more is made of them, in particular in the context of large cardinal axioms, where elementary embeddings of the whole set-theoretic universe are used to characterise the large cardinals. In this talk I will show how some of the power of elementary embeddings can be used in a category theory context. In particular, I will use this perspective in presenting a result with Joan Bagaria, in which we reduce the large cardinal assumption required to show that a (definable) full embedding into an accessible category must preserve lambda-directed colimits for some lambda.

This talk is part of the Category Theory Seminar series.

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