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Inaccessible cardinals and accessible categories

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Mathematical, Foundational and Computational Aspects of the Higher Infinite

There is a growing list of important questions in category theory, abstract homotopy theory or model theory where answers depend on large cardinals. These questions concern various properties of accessible categories which can be imagined as categories of models of infinitary first order theories. The answers depend on Vopenka’s principle or its consequences, mostly on the existence of a proper class of suitable large cardinals. We will give examples of such questions, explain their characteristic features and mention open problems.

This talk is part of the Isaac Newton Institute Seminar Series series.

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