University of Cambridge > Talks.cam > Category Theory Seminar > Commutation of Limits and Colimits -- a Cautionary Tale

Commutation of Limits and Colimits -- a Cautionary Tale

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The relation `limits of shape I commute with colimits of shape J in Set’ induces a Galois connection between classes of limit shapes and classes of colimit shapes, and it of some interest to determine the closed classes on either side. There are seven well-known closed classes for which the limit class is generated by finite categories (equivalently, for which the colimit class contains all filtered categories), and Martin Hyland’s student Marie Bjerrum conjectured that they were the only such classes. In the seminar I’ll describe the evidence which Marie produced in support of this conjecture, as well as the infinite family of counterexamples to it which I discovered the evening before her PhD viva.

This talk is part of the Category Theory Seminar series.

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