# Large cardinals, AECs and category theory

## Andrew Brooke-Taylor

### University of Bristol

Shelah’s Categoricity Conjecture is a central test question in the study of Abstract Elementary Classes (AECs) in model theory. Recently Boney has shown that under the assumption that sufficiently large strongly compact cardinals exist, the Shelah Categoricity Conjecture holds at successor cardinals. Lieberman and Rosicky have subsequently shown that AECs can be characterised in a very natural way in a category-theoretic setting, and with this perspective Boney’s result can actually be seen as a corollary of an old category-theoretic result of Makkai and Pare. Rosicky and I have now been able to improve upon this result of Makkai and Pare (and consequently Boney’s Theorem), obtaining it from α-strongly compact cardinals.

Andrew Brooke-Taylor is a set theorist, who applies large cardinal axioms and other tools and techniques from set theory to other areas of mathematics, particularly category theory and algebraic topology. He received his doctorate in 2007 from the Kurt Gödel Research Center and the Universität Wien, and has held postdoctoral positions at the University of Bristol and at Kobe University.